Grade 8 Algebra: Identifying Functions

Name: ______________________Date: ____________Score: ____ / 8

Level 1

Sets of ordered pairs

1. Is the relation a function:
$\{(1, 2), (2, 4), (3, 6)\}$
2. Is the relation a function:
$\{(1, 3), (1, 5), (2, 7)\}$
3. Is the relation a function:
$\{(0, 1), (1, 1), (2, 1)\}$
4. Is the relation a function:
$\{(2, 5), (3, 5), (2, 6)\}$
5. Is the relation a function:
$\{(-1, 4), (0, 3), (1, 2)\}$
6. Is the relation a function:
$\{(4, 1), (5, 2), (4, 3)\}$
7. Is the relation a function:
$\{(3, 0), (-3, 0), (6, 1)\}$
8. Is the relation a function:
$\{(7, 2), (8, 3), (9, 4)\}$

Answer Key

Level 1

1. $\text{Yes}$
2. $\text{No}\ (x = 1 \text{ twice})$
3. $\text{Yes}$
4. $\text{No}\ (x = 2 \text{ twice})$
5. $\text{Yes}$
6. $\text{No}\ (x = 4 \text{ twice})$
7. $\text{Yes}$
8. $\text{Yes}$

Grade 8 Algebra: Identifying Functions

Name: ______________________Date: ____________Score: ____ / 8

Level 2

Tables

1. Is the relation a function:
$\begin{array}{c|cccc} x & 1 & 2 & 3 & 4 \\ \hline y & 5 & 7 & 9 & 11 \end{array}$
2. Is the relation a function:
$\begin{array}{c|cccc} x & 1 & 1 & 2 & 3 \\ \hline y & 2 & 4 & 6 & 8 \end{array}$
3. Is the relation a function:
$\begin{array}{c|cccc} x & -2 & -1 & 0 & 1 \\ \hline y & 4 & 1 & 0 & 1 \end{array}$
4. Is the relation a function:
$\begin{array}{c|cccc} x & 0 & 1 & 2 & 2 \\ \hline y & 3 & 4 & 5 & 6 \end{array}$
5. Is the relation a function:
$\begin{array}{c|cccc} x & 5 & 5 & 5 & 5 \\ \hline y & 1 & 2 & 3 & 4 \end{array}$
6. Is the relation a function:
$\begin{array}{c|cccc} x & 1 & 2 & 3 & 4 \\ \hline y & 6 & 6 & 6 & 6 \end{array}$
7. Is the relation a function:
$\begin{array}{c|cccc} x & -1 & 0 & 1 & 0 \\ \hline y & 2 & 3 & 4 & 5 \end{array}$
8. Is the relation a function:
$\begin{array}{c|cccc} x & 2 & 4 & 6 & 8 \\ \hline y & 1 & 3 & 1 & 3 \end{array}$

Answer Key

Level 2

1. $\text{Yes}$
2. $\text{No}$
3. $\text{Yes}$
4. $\text{No}$
5. $\text{No}$
6. $\text{Yes}$
7. $\text{No}$
8. $\text{Yes}$

Grade 8 Algebra: Identifying Functions

Name: ______________________Date: ____________Score: ____ / 8

Level 3

Equations

1. Does the equation make ${y}$ a function of ${x}$ :
$y = 3x - 2$
2. Does the equation make ${y}$ a function of ${x}$ :
$x = 4$
3. Does the equation make ${y}$ a function of ${x}$ :
$y = x^2$
4. Does the equation make ${y}$ a function of ${x}$ :
$x = y^2$
5. Does the equation make ${y}$ a function of ${x}$ :
$y = 5$
6. Does the equation make ${y}$ a function of ${x}$ :
$x^2 + y^2 = 25$
7. Does the equation make ${y}$ a function of ${x}$ :
$y = |x|$
8. Does the equation make ${y}$ a function of ${x}$ :
$y = -2x + 7$

Answer Key

Level 3

1. $\text{Yes}$
2. $\text{No}$
3. $\text{Yes}$
4. $\text{No}\ (x = 4 \Rightarrow y = \pm 2)$
5. $\text{Yes}$
6. $\text{No}\ (x = 0 \Rightarrow y = \pm 5)$
7. $\text{Yes}$
8. $\text{Yes}$

Grade 8 Algebra: Evaluating Functions

Name: ______________________Date: ____________Score: ____ / 8

Level 1

Whole-number inputs

1. Evaluate:
$f(x) = x + 5;\ f(3)$
2. Evaluate:
$f(x) = 2x;\ f(6)$
3. Evaluate:
$f(x) = x - 4;\ f(10)$
4. Evaluate:
$f(x) = 3x + 1;\ f(2)$
5. Evaluate:
$f(x) = 5x - 3;\ f(4)$
6. Evaluate:
$f(x) = 10 - x;\ f(7)$
7. Evaluate:
$f(x) = 4x + 2;\ f(0)$
8. Evaluate:
$f(x) = \tfrac{x}{2} + 1;\ f(8)$

Answer Key

Level 1

1. $8$
2. $12$
3. $6$
4. $7$
5. $17$
6. $3$
7. $2$
8. $5$

Grade 8 Algebra: Evaluating Functions

Name: ______________________Date: ____________Score: ____ / 8

Level 2

Negatives, fractions and squares

1. Evaluate:
$f(x) = 2x + 3;\ f(-4)$
2. Evaluate:
$g(x) = -3x + 1;\ g(2)$
3. Evaluate:
$h(x) = x^2 + 1;\ h(-3)$
4. Evaluate:
$f(x) = \tfrac{1}{2}x - 2;\ f(-6)$
5. Evaluate:
$g(x) = x^2 - 2x;\ g(4)$
6. Evaluate:
$f(x) = -x + 8;\ f(-2)$
7. Evaluate:
$h(x) = \tfrac{3}{4}x;\ h(12)$
8. Evaluate:
$f(x) = 2x^2 - 5;\ f(3)$

Answer Key

Level 2

1. $-5$
2. $-5$
3. $10$
4. $-5$
5. $8$
6. $10$
7. $9$
8. $13$

Grade 8 Algebra: Evaluating Functions

Name: ______________________Date: ____________Score: ____ / 8

Level 3

Solving and combining

1. Find ${x}$ :
$f(x) = 2x + 3;\ f(x) = 11$
2. Find ${x}$ :
$f(x) = 5x - 7;\ f(x) = -2$
3. Find ${x}$ :
$g(x) = -4x + 6;\ g(x) = 18$
4. Evaluate:
$f(x) = 3x - 1;\ f(2) + f(-1)$
5. Evaluate:
$f(x) = x^2,\ g(x) = 2x + 1;\ f(3) - g(3)$
6. Find ${x}$ :
$f(x) = \tfrac{x}{3} + 4;\ f(x) = 6$
7. Evaluate:
$f(x) = 2x - 1;\ f(f(2))$
8. Find ${x}$ :
$f(x) = -2x + 9;\ f(x) = x$

Answer Key

Level 3

1. $x = 4$
2. $x = 1$
3. $x = -3$
4. $1$
5. $2$
6. $x = 6$
7. $5$
8. $x = 3$

Grade 8 Algebra: Linear and Nonlinear Functions

Name: ______________________Date: ____________Score: ____ / 8

Level 1

Equations

1. Linear or nonlinear:
$y = 4x - 1$
2. Linear or nonlinear:
$y = x^2$
3. Linear or nonlinear:
$y = -x + 3$
4. Linear or nonlinear:
$y = \dfrac{1}{x}$
5. Linear or nonlinear:
$y = 7$
6. Linear or nonlinear:
$y = x^3$
7. Linear or nonlinear:
$y = \tfrac{1}{2}x$
8. Linear or nonlinear:
$y = 2^x$

Answer Key

Level 1

1. $\text{Linear}$
2. $\text{Nonlinear}$
3. $\text{Linear}$
4. $\text{Nonlinear}$
5. $\text{Linear}$
6. $\text{Nonlinear}$
7. $\text{Linear}$
8. $\text{Nonlinear}$

Grade 8 Algebra: Linear and Nonlinear Functions

Name: ______________________Date: ____________Score: ____ / 8

Level 2

Tables

1. Linear or nonlinear:
$\begin{array}{c|cccc} x & 0 & 1 & 2 & 3 \\ \hline y & 1 & 3 & 5 & 7 \end{array}$
2. Linear or nonlinear:
$\begin{array}{c|cccc} x & 0 & 1 & 2 & 3 \\ \hline y & 0 & 1 & 4 & 9 \end{array}$
3. Linear or nonlinear:
$\begin{array}{c|cccc} x & 1 & 2 & 3 & 4 \\ \hline y & 10 & 7 & 4 & 1 \end{array}$
4. Linear or nonlinear:
$\begin{array}{c|cccc} x & 1 & 2 & 3 & 4 \\ \hline y & 2 & 4 & 8 & 16 \end{array}$
5. Linear or nonlinear:
$\begin{array}{c|cccc} x & 0 & 2 & 4 & 6 \\ \hline y & 5 & 6 & 7 & 8 \end{array}$
6. Linear or nonlinear:
$\begin{array}{c|cccc} x & -1 & 0 & 1 & 2 \\ \hline y & 1 & 0 & 1 & 4 \end{array}$
7. Linear or nonlinear:
$\begin{array}{c|cccc} x & 2 & 4 & 6 & 8 \\ \hline y & 3 & 3 & 3 & 3 \end{array}$
8. Linear or nonlinear:
$\begin{array}{c|cccc} x & 0 & 1 & 3 & 4 \\ \hline y & 2 & 4 & 8 & 10 \end{array}$

Answer Key

Level 2

1. $\text{Linear}\ (+2)$
2. $\text{Nonlinear}$
3. $\text{Linear}\ (-3)$
4. $\text{Nonlinear}$
5. $\text{Linear}\ (\tfrac{1}{2})$
6. $\text{Nonlinear}$
7. $\text{Linear}\ (0)$
8. $\text{Linear}\ (2)$

Grade 8 Algebra: Linear and Nonlinear Functions

Name: ______________________Date: ____________Score: ____ / 8

Level 3

Rewrite first

1. Linear or nonlinear:
$2x + y = 6$
2. Linear or nonlinear:
$y = x(x + 1)$
3. Linear or nonlinear:
$y - 3 = 2(x + 1)$
4. Linear or nonlinear:
$xy = 12$
5. Linear or nonlinear:
$y = \dfrac{x + 4}{2}$
6. Linear or nonlinear:
$y = 3x^2 - 3x^2 + 5x$
7. Linear or nonlinear:
$y = (x + 2)^2 - x^2$
8. Linear or nonlinear:
$y = \dfrac{6}{x} + 1$

Answer Key

Level 3

1. $\text{Linear}\ (y = -2x + 6)$
2. $\text{Nonlinear}\ (x^2 + x)$
3. $\text{Linear}\ (y = 2x + 5)$
4. $\text{Nonlinear}$
5. $\text{Linear}\ (y = \tfrac{1}{2}x + 2)$
6. $\text{Linear}\ (y = 5x)$
7. $\text{Linear}\ (y = 4x + 4)$
8. $\text{Nonlinear}$

Grade 8 Algebra: Comparing Functions

Name: ______________________Date: ____________Score: ____ / 8

Level 1

Greater rate of change

1. Which has the greater rate of change:
$\begin{array}{ll} \textbf{A:} & y = 3x + 1 \\[14pt] \textbf{B:} & \begin{array}{c|ccc} x & 0 & 1 & 2 \\ \hline y & 2 & 4 & 6 \end{array} \end{array}$
2. Which has the greater rate of change:
$\begin{array}{ll} \textbf{A:} & y = 2x + 5 \\[14pt] \textbf{B:} & \begin{array}{c|ccc} x & 0 & 1 & 2 \\ \hline y & 1 & 5 & 9 \end{array} \end{array}$
3. Which has the greater rate of change:
$\begin{array}{ll} \textbf{A:} & y = -x + 4 \\[14pt] \textbf{B:} & \begin{array}{c|ccc} x & 0 & 1 & 2 \\ \hline y & 0 & 2 & 4 \end{array} \end{array}$
4. Which has the greater rate of change:
$\begin{array}{ll} \textbf{A:} & y = 5x \\[14pt] \textbf{B:} & \begin{array}{c|ccc} x & 0 & 2 & 4 \\ \hline y & 3 & 13 & 23 \end{array} \end{array}$
5. Which has the greater rate of change:
$\begin{array}{ll} \textbf{A:} & y = x + 6 \\[14pt] \textbf{B:} & \begin{array}{c|ccc} x & 1 & 2 & 3 \\ \hline y & 3 & 6 & 9 \end{array} \end{array}$
6. Which has the greater rate of change:
$\begin{array}{ll} \textbf{A:} & y = 4x - 2 \\[14pt] \textbf{B:} & \begin{array}{c|ccc} x & 0 & 1 & 2 \\ \hline y & 7 & 10 & 13 \end{array} \end{array}$
7. Which has the greater rate of change:
$\begin{array}{ll} \textbf{A:} & y = \tfrac{1}{2}x \\[14pt] \textbf{B:} & \begin{array}{c|ccc} x & 0 & 4 & 8 \\ \hline y & 0 & 1 & 2 \end{array} \end{array}$
8. Which has the greater rate of change:
$\begin{array}{ll} \textbf{A:} & y = 6x + 1 \\[14pt] \textbf{B:} & \begin{array}{c|ccc} x & 2 & 3 & 4 \\ \hline y & 8 & 14 & 20 \end{array} \end{array}$

Answer Key

Level 1

1. $\text{A } (3 > 2)$
2. $\text{B } (4 > 2)$
3. $\text{B } (2 > -1)$
4. $\text{Same } (5)$
5. $\text{B } (3 > 1)$
6. $\text{A } (4 > 3)$
7. $\text{A } (\tfrac12 > \tfrac14)$
8. $\text{Same } (6)$

Grade 8 Algebra: Comparing Functions

Name: ______________________Date: ____________Score: ____ / 8

Level 2

Greater initial value

1. Which has the greater initial value:
$\begin{array}{ll} \textbf{A:} & y = 2x + 7 \\[14pt] \textbf{B:} & \begin{array}{c|ccc} x & 0 & 1 & 2 \\ \hline y & 4 & 6 & 8 \end{array} \end{array}$
2. Which has the greater initial value:
$\begin{array}{ll} \textbf{A:} & y = -3x + 2 \\[14pt] \textbf{B:} & \begin{array}{c|ccc} x & 0 & 1 & 2 \\ \hline y & 5 & 2 & -1 \end{array} \end{array}$
3. Which has the greater initial value:
$\begin{array}{ll} \textbf{A:} & y = x - 4 \\[14pt] \textbf{B:} & \begin{array}{c|ccc} x & 1 & 2 & 3 \\ \hline y & 0 & 1 & 2 \end{array} \end{array}$
4. Which has the greater initial value:
$\begin{array}{ll} \textbf{A:} & y = 4x + 3 \\[14pt] \textbf{B:} & \begin{array}{c|ccc} x & 1 & 2 & 3 \\ \hline y & 5 & 7 & 9 \end{array} \end{array}$
5. Which has the greater initial value:
$\begin{array}{ll} \textbf{A:} & y = \tfrac{1}{2}x + 6 \\[14pt] \textbf{B:} & \begin{array}{c|ccc} x & 2 & 4 & 6 \\ \hline y & 9 & 10 & 11 \end{array} \end{array}$
6. Which has the greater initial value:
$\begin{array}{ll} \textbf{A:} & y = -2x + 10 \\[14pt] \textbf{B:} & \begin{array}{c|ccc} x & 1 & 2 & 3 \\ \hline y & 11 & 14 & 17 \end{array} \end{array}$
7. Which has the greater initial value:
$\begin{array}{ll} \textbf{A:} & y = 5x \\[14pt] \textbf{B:} & \begin{array}{c|ccc} x & 1 & 2 & 3 \\ \hline y & 2 & 1 & 0 \end{array} \end{array}$
8. Which has the greater initial value:
$\begin{array}{ll} \textbf{A:} & y = 3x - 1 \\[14pt] \textbf{B:} & \begin{array}{c|ccc} x & -1 & 0 & 1 \\ \hline y & -6 & -2 & 2 \end{array} \end{array}$

Answer Key

Level 2

1. $\text{A } (7 > 4)$
2. $\text{B } (5 > 2)$
3. $\text{B } (-1 > -4)$
4. $\text{Same } (3)$
5. $\text{B } (8 > 6)$
6. $\text{A } (10 > 8)$
7. $\text{B } (3 > 0)$
8. $\text{A } (-1 > -2)$

Grade 8 Algebra: Comparing Functions

Name: ______________________Date: ____________Score: ____ / 8

Level 3

Real-life comparisons

1. ${x}$ = hours, ${y}$ = miles. Which car is faster:
$\begin{array}{ll} \textbf{A:} & y = 55x \\[14pt] \textbf{B:} & \begin{array}{c|ccc} x & 1 & 2 & 3 \\ \hline y & 60 & 120 & 180 \end{array} \end{array}$
2. ${x}$ = months, ${y}$ = total cost in dollars. Which gym has the lower joining fee:
$\begin{array}{ll} \textbf{A:} & y = 30x + 50 \\[14pt] \textbf{B:} & \begin{array}{c|ccc} x & 1 & 2 & 3 \\ \hline y & 65 & 100 & 135 \end{array} \end{array}$
3. ${x}$ = months, ${y}$ = total cost in dollars. Which gym costs less per month:
$\begin{array}{ll} \textbf{A:} & y = 30x + 50 \\[14pt] \textbf{B:} & \begin{array}{c|ccc} x & 1 & 2 & 3 \\ \hline y & 65 & 100 & 135 \end{array} \end{array}$
4. ${x}$ = weeks, ${y}$ = dollars saved. Who saves more each week:
$\begin{array}{ll} \textbf{A:} & y = 15x + 20 \\[14pt] \textbf{B:} & \begin{array}{c|ccc} x & 0 & 2 & 4 \\ \hline y & 40 & 64 & 88 \end{array} \end{array}$
5. ${x}$ = minutes, ${y}$ = liters left. Which tank drains faster:
$\begin{array}{ll} \textbf{A:} & y = -4x + 100 \\[14pt] \textbf{B:} & \begin{array}{c|ccc} x & 0 & 5 & 10 \\ \hline y & 80 & 55 & 30 \end{array} \end{array}$
6. ${x}$ = minutes, ${y}$ = liters left. Which tank starts with more water:
$\begin{array}{ll} \textbf{A:} & y = -4x + 100 \\[14pt] \textbf{B:} & \begin{array}{c|ccc} x & 0 & 5 & 10 \\ \hline y & 80 & 55 & 30 \end{array} \end{array}$
7. ${x}$ = weeks, ${y}$ = height in cm. Which plant grows faster:
$\begin{array}{ll} \textbf{A:} & y = 0.5x + 12 \\[14pt] \textbf{B:} & (2, 10),\ (6, 13) \end{array}$
8. ${x}$ = texts, ${y}$ = cost in dollars. When do the plans cost the same:
$\begin{array}{ll} \textbf{A:} & y = 0.1x + 20 \\[14pt] \textbf{B:} & \begin{array}{c|ccc} x & 0 & 100 & 200 \\ \hline y & 10 & 40 & 70 \end{array} \end{array}$

Answer Key

Level 3

1. $\text{B } (60\text{ mph})$
2. $\text{B } (\$30)$
3. $\text{A } (\$30 < \$35)$
4. $\text{A } (\$15 > \$12)$
5. $\text{B } (5\text{ L/min})$
6. $\text{A } (100\text{ L})$
7. $\text{B } (0.75 > 0.5)$
8. $50\text{ texts, }\$25$

Grade 8 Algebra: Word Problems: Functions

Name: ______________________Date: ____________Score: ____ / 8

Level 1

Write and evaluate

1. Solve:
$\text{Pizzas}$ $\text{cost}$ $\text{8}$ $\text{dollars}$ $\text{each.}$ $\text{Write}$ $\text{a}$ $\text{function}$ $\text{for}$ $\text{the}$ $\text{cost}$ $\text{of}$ $p\text{}$ $\text{pizzas.}$
2. Solve:
$\text{A}$ $\text{taxi}$ $\text{charges}$ $\text{3}$ $\text{dollars}$ $\text{plus}$ $\text{2}$ $\text{dollars}$ $\text{per}$ $\text{mile.}$ $\text{Write}$ $\text{a}$ $\text{function}$ $\text{for}$ $\text{the}$ $\text{cost}$ $\text{of}$ $m\text{}$ $\text{miles.}$
3. Solve:
$\text{A}$ $\text{candle}$ $\text{is}$ $\text{20}$ $\text{cm}$ $\text{tall}$ $\text{and}$ $\text{burns}$ $\text{2}$ $\text{cm}$ $\text{per}$ $\text{hour.}$ $\text{Write}$ $\text{a}$ $\text{function}$ $\text{for}$ $\text{its}$ $\text{height}$ $\text{after}$ $h\text{}$ $\text{hours.}$
4. Solve:
$\text{A}$ $\text{plumber}$ $\text{charges}$ $\text{40}$ $\text{dollars}$ $\text{plus}$ $\text{25}$ $\text{dollars}$ $\text{per}$ $\text{hour.}$ $\text{What}$ $\text{is}$ $\text{the}$ $\text{charge}$ $\text{for}$ $\text{3}$ $\text{hours?}$
5. Solve:
$\text{A}$ $\text{phone}$ $\text{has}$ $\text{80}$ $\text{percent}$ $\text{battery}$ $\text{and}$ $\text{loses}$ $\text{5}$ $\text{percent}$ $\text{per}$ $\text{hour.}$ $\text{What}$ $\text{is}$ $\text{the}$ $\text{battery}$ $\text{after}$ $\text{6}$ $\text{hours?}$
6. Solve:
$\text{A}$ $\text{pool}$ $\text{has}$ $\text{200}$ $\text{liters}$ $\text{and}$ $\text{fills}$ $\text{at}$ $\text{30}$ $\text{liters}$ $\text{per}$ $\text{minute.}$ $\text{How}$ $\text{much}$ $\text{water}$ $\text{is}$ $\text{in}$ $\text{it}$ $\text{after}$ $\text{4}$ $\text{minutes?}$
7. Solve:
$\text{Movie}$ $\text{tickets}$ $\text{cost}$ $\text{12}$ $\text{dollars}$ $\text{each.}$ $\text{What}$ $\text{is}$ $\text{the}$ $\text{cost}$ $\text{of}$ $\text{5}$ $\text{tickets?}$
8. Solve:
$\text{A}$ $\text{plant}$ $\text{is}$ $\text{5}$ $\text{cm}$ $\text{tall}$ $\text{and}$ $\text{grows}$ $\text{3}$ $\text{cm}$ $\text{per}$ $\text{week.}$ $\text{How}$ $\text{tall}$ $\text{is}$ $\text{it}$ $\text{after}$ $\text{7}$ $\text{weeks?}$

Answer Key

Level 1

1. $C = 8p$
2. $C = 2m + 3$
3. $H = 20 - 2h$
4. $\$115$
5. $50\%$
6. $320\text{ L}$
7. $\$60$
8. $26\text{ cm}$

Grade 8 Algebra: Word Problems: Functions

Name: ______________________Date: ____________Score: ____ / 8

Level 2

Interpret a function rule

1. Use ${C = 4h + 10}$ :
$C\text{}$ $\text{is}$ $\text{the}$ $\text{cost}$ $\text{in}$ $\text{dollars}$ $\text{to}$ $\text{rent}$ $\text{a}$ $\text{bike}$ $\text{for}$ $h\text{}$ $\text{hours.}$ $\text{What}$ $\text{do}$ $\text{the}$ $\text{4}$ $\text{and}$ $\text{the}$ $\text{10}$ $\text{mean?}$
2. Use ${T = 2m + 15}$ :
$T\text{}$ $\text{is}$ $\text{the}$ $\text{water}$ $\text{temperature}$ $\text{in}$ $\text{degrees}$ $\text{after}$ $m\text{}$ $\text{minutes}$ $\text{of}$ $\text{heating.}$ $\text{What}$ $\text{is}$ $\text{it}$ $\text{after}$ $\text{10}$ $\text{minutes?}$
3. Use ${d = 60t}$ :
$d\text{}$ $\text{is}$ $\text{the}$ $\text{distance}$ $\text{in}$ $\text{miles}$ $\text{a}$ $\text{train}$ $\text{goes}$ $\text{in}$ $t\text{}$ $\text{hours.}$ $\text{How}$ $\text{long}$ $\text{does}$ $\text{it}$ $\text{take}$ $\text{to}$ $\text{go}$ $\text{210}$ $\text{miles?}$
4. Use ${B = 500 - 25w}$ :
$B\text{}$ $\text{is}$ $\text{the}$ $\text{money}$ $\text{left}$ $\text{in}$ $\text{dollars}$ $\text{after}$ $w\text{}$ $\text{weeks.}$ $\text{After}$ $\text{how}$ $\text{many}$ $\text{weeks}$ $\text{is}$ $\text{the}$ $\text{money}$ $\text{gone?}$
5. Use ${P = 15n - 60}$ :
$P\text{}$ $\text{is}$ $\text{the}$ $\text{profit}$ $\text{in}$ $\text{dollars}$ $\text{from}$ $\text{selling}$ $n\text{}$ $\text{shirts.}$ $\text{How}$ $\text{many}$ $\text{shirts}$ $\text{must}$ $\text{be}$ $\text{sold}$ $\text{to}$ $\text{break}$ $\text{even?}$
6. Use ${H = 3w + 5}$ :
$H\text{}$ $\text{is}$ $\text{a}$ $\text{plant's}$ $\text{height}$ $\text{in}$ $\text{cm}$ $\text{after}$ $w\text{}$ $\text{weeks.}$ $\text{When}$ $\text{is}$ $\text{it}$ $\text{29}$ $\text{cm}$ $\text{tall?}$
7. Use ${C = 0.5m + 20}$ :
$C\text{}$ $\text{is}$ $\text{the}$ $\text{monthly}$ $\text{phone}$ $\text{cost}$ $\text{in}$ $\text{dollars}$ $\text{for}$ $m\text{}$ $\text{minutes.}$ $\text{What}$ $\text{is}$ $\text{the}$ $\text{cost}$ $\text{for}$ $\text{100}$ $\text{minutes?}$
8. Use ${V = 1200 - 150y}$ :
$V\text{}$ $\text{is}$ $\text{a}$ $\text{laptop's}$ $\text{value}$ $\text{in}$ $\text{dollars}$ $\text{after}$ $y\text{}$ $\text{years.}$ $\text{What}$ $\text{is}$ $\text{it}$ $\text{worth}$ $\text{after}$ $\text{4}$ $\text{years?}$

Answer Key

Level 2

1. $\$4\text{/hour; }\$10\text{ fee}$
2. $35^\circ$
3. $3.5\text{ hours}$
4. $20\text{ weeks}$
5. $4\text{ shirts}$
6. $8\text{ weeks}$
7. $\$70$
8. $\$600$

Grade 8 Algebra: Word Problems: Functions

Name: ______________________Date: ____________Score: ____ / 8

Level 3

Build the function

1. Solve:
$\text{A}$ $\text{gym}$ $\text{charges}$ $\text{a}$ $\text{40}$ $\text{dollar}$ $\text{joining}$ $\text{fee}$ $\text{plus}$ $\text{25}$ $\text{dollars}$ $\text{per}$ $\text{month.}$ $\text{Write}$ $\text{a}$ $\text{function}$ $\text{for}$ $m\text{}$ $\text{months}$ $\text{and}$ $\text{find}$ $\text{the}$ $\text{cost}$ $\text{for}$ $\text{1}$ $\text{year.}$
2. Solve:
$\text{A}$ $\text{tank}$ $\text{holds}$ $\text{90}$ $\text{liters}$ $\text{and}$ $\text{drains}$ $\text{6}$ $\text{liters}$ $\text{per}$ $\text{minute.}$ $\text{Write}$ $\text{a}$ $\text{function}$ $\text{for}$ $t\text{}$ $\text{minutes}$ $\text{and}$ $\text{find}$ $\text{when}$ $\text{it}$ $\text{is}$ $\text{empty.}$
3. Solve:
$\text{A}$ $\text{4}$ $\text{mile}$ $\text{taxi}$ $\text{ride}$ $\text{costs}$ $\text{11}$ $\text{dollars}$ $\text{and}$ $\text{a}$ $\text{10}$ $\text{mile}$ $\text{ride}$ $\text{costs}$ $\text{23}$ $\text{dollars.}$ $\text{Write}$ $\text{a}$ $\text{linear}$ $\text{function}$ $\text{for}$ $\text{the}$ $\text{cost}$ $\text{of}$ $m\text{}$ $\text{miles.}$
4. Solve:
$\text{A}$ $\text{plant}$ $\text{is}$ $\text{8}$ $\text{cm}$ $\text{tall}$ $\text{after}$ $\text{2}$ $\text{weeks}$ $\text{and}$ $\text{14}$ $\text{cm}$ $\text{tall}$ $\text{after}$ $\text{5}$ $\text{weeks.}$ $\text{Write}$ $\text{a}$ $\text{function}$ $\text{for}$ $w\text{}$ $\text{weeks}$ $\text{and}$ $\text{find}$ $\text{its}$ $\text{height}$ $\text{at}$ $\text{planting.}$
5. Solve:
$\text{Plan}$ $\text{A}$ $\text{costs}$ $\text{30}$ $\text{dollars}$ $\text{plus}$ $\text{5}$ $\text{dollars}$ $\text{per}$ $\text{class.}$ $\text{Plan}$ $B\text{}$ $\text{costs}$ $\text{10}$ $\text{dollars}$ $\text{per}$ $\text{class.}$ $\text{For}$ $\text{how}$ $\text{many}$ $\text{classes}$ $\text{do}$ $\text{they}$ $\text{cost}$ $\text{the}$ $\text{same?}$
6. Solve:
$\text{A}$ $\text{car}$ $\text{has}$ $\text{50}$ $\text{liters}$ $\text{of}$ $\text{fuel}$ $\text{and}$ $\text{uses}$ $\text{4}$ $\text{liters}$ $\text{every}$ $\text{50}$ $\text{km.}$ $\text{How}$ $\text{much}$ $\text{fuel}$ $\text{is}$ $\text{left}$ $\text{after}$ $\text{300}$ $\text{km?}$
7. Solve:
$\text{An}$ $\text{empty}$ $\text{bucket}$ $\text{weighs}$ $\text{2}$ $\text{kg}$ $\text{and}$ $\text{each}$ $\text{liter}$ $\text{of}$ $\text{water}$ $\text{adds}$ $\text{1}$ $\text{kg.}$ $\text{Write}$ $\text{a}$ $\text{function}$ $\text{for}$ $x\text{}$ $\text{liters}$ $\text{and}$ $\text{find}$ $\text{the}$ $\text{weight}$ $\text{with}$ $\text{7}$ $\text{liters.}$
8. Solve:
$\text{A}$ $\text{printer}$ $\text{warms}$ $\text{up}$ $\text{for}$ $\text{1}$ $\text{minute,}$ $\text{then}$ $\text{prints}$ $\text{18}$ $\text{pages}$ $\text{per}$ $\text{minute.}$ $\text{How}$ $\text{many}$ $\text{pages}$ $\text{are}$ $\text{printed}$ $\text{in}$ $\text{6}$ $\text{minutes?}$

Answer Key

Level 3

1. $C = 25m + 40;\ \$340$
2. $V = 90 - 6t;\ 15\text{ min}$
3. $C = 2m + 3$
4. $H = 2w + 4;\ 4\text{ cm}$
5. $6\text{ classes}$
6. $26\text{ L}$
7. $W = x + 2;\ 9\text{ kg}$
8. $90\text{ pages}$

Grade 8 Algebra: Identifying Functions from Graphs

Name: ______________________Date: ____________Score: ____ / 8

Level 1

Lines and familiar curves

Directions: Use the vertical line test to decide whether each graph represents a function of ${x}$ .

1.
2.
3.
4.
5.
6.
7.
8.

Answer Key

Level 1

1. $\text{Yes: passes the vertical line test}$
2. $\text{No: fails the vertical line test}$
3. $\text{Yes: passes the vertical line test}$
4. $\text{No: fails the vertical line test}$
5. $\text{Yes: passes the vertical line test}$
6. $\text{No: fails the vertical line test}$
7. $\text{Yes: passes the vertical line test}$
8. $\text{Yes: passes the vertical line test}$

Grade 8 Algebra: Identifying Functions from Graphs

Name: ______________________Date: ____________Score: ____ / 8

Level 2

Discrete points

Directions: Use the vertical line test to decide whether each graph represents a function of ${x}$ .

1.
2.
3.
4.
5.
6.
7.
8.

Answer Key

Level 2

1. $\text{Yes: passes the vertical line test}$
2. $\text{No: fails the vertical line test}$
3. $\text{Yes: passes the vertical line test}$
4. $\text{No: fails the vertical line test}$
5. $\text{Yes: passes the vertical line test}$
6. $\text{No: fails the vertical line test}$
7. $\text{Yes: passes the vertical line test}$
8. $\text{Yes: passes the vertical line test}$

Grade 8 Algebra: Identifying Functions from Graphs

Name: ______________________Date: ____________Score: ____ / 8

Level 3

Shifted curves and relations

Directions: Use the vertical line test to decide whether each graph represents a function of ${x}$ .

1.
2.
3.
4.
5.
6.
7.
8.

Answer Key

Level 3

1. $\text{Yes: passes the vertical line test}$
2. $\text{No: fails the vertical line test}$
3. $\text{No: fails the vertical line test}$
4. $\text{Yes: passes the vertical line test}$
5. $\text{No: fails the vertical line test}$
6. $\text{Yes: passes the vertical line test}$
7. $\text{No: fails the vertical line test}$
8. $\text{Yes: passes the vertical line test}$

Grade 8 Algebra: Linear and Nonlinear Graphs

Name: ______________________Date: ____________Score: ____ / 8

Level 1

Straight lines and curves

Directions: Classify each function graph as linear or nonlinear. Explain your choice.

1.
2.
3.
4.
5.
6.
7.
8.

Answer Key

Level 1

1. $\text{Linear: straight line}$
2. $\text{Nonlinear: not a straight line}$
3. $\text{Linear: straight line}$
4. $\text{Nonlinear: not a straight line}$
5. $\text{Linear: straight line}$
6. $\text{Nonlinear: not a straight line}$
7. $\text{Linear: straight line}$
8. $\text{Nonlinear: not a straight line}$

Grade 8 Algebra: Linear and Nonlinear Graphs

Name: ______________________Date: ____________Score: ____ / 8

Level 2

Shifted graphs

Directions: Classify each function graph as linear or nonlinear. Explain your choice.

1.
2.
3.
4.
5.
6.
7.
8.

Answer Key

Level 2

1. $\text{Linear: straight line}$
2. $\text{Nonlinear: not a straight line}$
3. $\text{Nonlinear: not a straight line}$
4. $\text{Linear: straight line}$
5. $\text{Linear: straight line}$
6. $\text{Nonlinear: not a straight line}$
7. $\text{Linear: straight line}$
8. $\text{Nonlinear: not a straight line}$

Grade 8 Algebra: Linear and Nonlinear Graphs

Name: ______________________Date: ____________Score: ____ / 8

Level 3

Piecewise and less familiar graphs

Directions: Classify each function graph as linear or nonlinear. Explain your choice.

1.
2.
3.
4.
5.
6.
7.
8.

Answer Key

Level 3

1. $\text{Nonlinear: not a straight line}$
2. $\text{Linear: straight line}$
3. $\text{Nonlinear: not a straight line}$
4. $\text{Linear: straight line}$
5. $\text{Nonlinear: not a straight line}$
6. $\text{Linear: straight line}$
7. $\text{Nonlinear: not a straight line}$
8. $\text{Linear: straight line}$

Grade 8 Algebra: Reading Values from Function Graphs

Name: ______________________Date: ____________Score: ____ / 8

Level 1

Read outputs from lines

Directions: Read each value from the graph. Each grid step is one unit.

1.
$f(2) = \ ?$
2.
$f(1) = \ ?$
3.
$f(2) = \ ?$
4.
$f(4) = \ ?$
5.
$f(-1) = \ ?$
6.
$f(-2) = \ ?$
7.
$f(4) = \ ?$
8.
$f(-4) = \ ?$

Answer Key

Level 1

1. $3$
2. $2$
3. $3$
4. $3$
5. $3$
6. $-4$
7. $3$
8. $2$

Grade 8 Algebra: Reading Values from Function Graphs

Name: ______________________Date: ____________Score: ____ / 8

Level 2

Read outputs from curves

Directions: Read each value from the graph. Each grid step is one unit.

1.
$f(2) = \ ?$
2.
$f(-3) = \ ?$
3.
$f(1) = \ ?$
4.
$f(3) = \ ?$
5.
$f(-2) = \ ?$
6.
$f(2) = \ ?$
7.
$f(2) = \ ?$
8.
$f(-4) = \ ?$

Answer Key

Level 2

1. $4$
2. $3$
3. $3$
4. $2$
5. $3$
6. $1$
7. $2$
8. $-1$

Grade 8 Algebra: Reading Values from Function Graphs

Name: ______________________Date: ____________Score: ____ / 8

Level 3

Find inputs and compare outputs

Directions: Read each value from the graph. Each grid step is one unit.

1.
$f(x) = 4;\quad x = \ ?$
2.
$f(x) = 4;\quad x = \ ?$
3.
$f(x) = 1;\quad x = \ ?$
4.
$f(x) = -1;\quad x = \ ?$
5.
$f(x) = 4;\quad \text{find all }x$
6.
$f(x) = 0;\quad \text{find all }x$
7.
$f(3)-f(1)$
8.
$f(-2)+f(2)$

Answer Key

Level 3

1. $x = 3$
2. $x = -2$
3. $x = 1$
4. $x = -4$
5. $x=-2, 2$
6. $x=-2, 2$
7. $2$
8. $2$

Grade 8 Algebra: Interpreting Function Graphs

Name: ______________________Date: ____________Score: ____ / 8

Level 1

Initial values and changes

Directions: Read the graph in each context. The horizontal axis is time t; the vertical axis is the stated quantity.

1.
$\text{Water}$ $\text{in}$ $\text{liters,}$ $\text{time}$ $\text{in}$ $\text{minutes.}$ $\text{How}$ $\text{much}$ $\text{water}$ $\text{is}$ $\text{there}$ $\text{initially?}$
2.
$\text{Water}$ $\text{in}$ $\text{liters,}$ $\text{time}$ $\text{in}$ $\text{minutes.}$ $\text{When}$ $\text{is}$ $\text{the}$ $\text{tank}$ $\text{empty?}$
3.
$\text{Height}$ $\text{in}$ $\text{cm,}$ $\text{time}$ $\text{in}$ $\text{weeks.}$ $\text{What}$ $\text{is}$ $\text{the}$ $\text{initial}$ $\text{height?}$
4.
$\text{Height}$ $\text{in}$ $\text{cm,}$ $\text{time}$ $\text{in}$ $\text{weeks.}$ $\text{What}$ $\text{is}$ $\text{the}$ $\text{height}$ $\text{at}$ $\text{3}$ $\text{weeks?}$
5.
$\text{Savings}$ $\text{in}$ $\text{dollars,}$ $\text{time}$ $\text{in}$ $\text{weeks.}$ $\text{How}$ $\text{much}$ $\text{is}$ $\text{saved}$ $\text{initially?}$
6.
$\text{Savings}$ $\text{in}$ $\text{dollars,}$ $\text{time}$ $\text{in}$ $\text{weeks.}$ $\text{How}$ $\text{much}$ $\text{is}$ $\text{saved}$ $\text{at}$ $\text{2}$ $\text{weeks?}$
7.
$\text{Water}$ $\text{in}$ $\text{liters,}$ $\text{time}$ $\text{in}$ $\text{minutes.}$ $\text{How}$ $\text{much}$ $\text{is}$ $\text{left}$ $\text{after}$ $\text{1}$ $\text{minute?}$
8.
$\text{Height}$ $\text{in}$ $\text{cm,}$ $\text{time}$ $\text{in}$ $\text{weeks.}$ $\text{How}$ $\text{much}$ $\text{does}$ $\text{the}$ $\text{height}$ $\text{increase}$ $\text{in}$ $\text{4}$ $\text{weeks?}$

Answer Key

Level 1

1. $8\text{ L}$
2. $4\text{ min}$
3. $2\text{ cm}$
4. $5\text{ cm}$
5. $\$10$
6. $\$20$
7. $6\text{ L}$
8. $4\text{ cm}$

Grade 8 Algebra: Interpreting Function Graphs

Name: ______________________Date: ____________Score: ____ / 8

Level 2

Increasing, decreasing and constant

Directions: Read the graph in each context. The horizontal axis is time t; the vertical axis is the stated quantity.

1.
$\text{Distance}$ $\text{from}$ $\text{home}$ $\text{in}$ $\text{km,}$ $\text{time}$ $\text{in}$ $\text{hours.}$ $\text{When}$ $\text{is}$ $\text{the}$ $\text{person}$ $\text{moving}$ $\text{away?}$
2.
$\text{Distance}$ $\text{from}$ $\text{home}$ $\text{in}$ $\text{km,}$ $\text{time}$ $\text{in}$ $\text{hours.}$ $\text{When}$ $\text{is}$ $\text{the}$ $\text{person}$ $\text{stationary?}$
3.
$\text{Distance}$ $\text{from}$ $\text{home}$ $\text{in}$ $\text{km,}$ $\text{time}$ $\text{in}$ $\text{hours.}$ $\text{When}$ $\text{is}$ $\text{the}$ $\text{person}$ $\text{returning?}$
4.
$\text{Distance}$ $\text{from}$ $\text{home}$ $\text{in}$ $\text{km,}$ $\text{time}$ $\text{in}$ $\text{hours.}$ $\text{What}$ $\text{is}$ $\text{the}$ $\text{greatest}$ $\text{distance?}$
5.
$\text{Temperature}$ $\text{in}$ $\text{degrees}$ $\text{Celsius,}$ $\text{time}$ $\text{in}$ $\text{minutes.}$ $\text{When}$ $\text{is}$ $\text{it}$ $\text{increasing?}$
6.
$\text{Temperature}$ $\text{in}$ $\text{degrees}$ $\text{Celsius,}$ $\text{time}$ $\text{in}$ $\text{minutes.}$ $\text{When}$ $\text{is}$ $\text{it}$ $\text{constant?}$
7.
$\text{Temperature}$ $\text{in}$ $\text{degrees}$ $\text{Celsius,}$ $\text{time}$ $\text{in}$ $\text{minutes.}$ $\text{When}$ $\text{is}$ $\text{it}$ $\text{decreasing?}$
8.
$\text{Temperature}$ $\text{in}$ $\text{degrees}$ $\text{Celsius,}$ $\text{time}$ $\text{in}$ $\text{minutes.}$ $\text{What}$ $\text{is}$ $\text{it}$ $\text{at}$ $\text{5}$ $\text{minutes?}$

Answer Key

Level 2

1. $0<t<2$
2. $2<t<4$
3. $4<t<6$
4. $4\text{ km}$
5. $0<t<2$
6. $2<t<4$
7. $4<t<6$
8. $25^\circ\text{C}$

Grade 8 Algebra: Interpreting Function Graphs

Name: ______________________Date: ____________Score: ____ / 8

Level 3

Rates, intervals and rules

Directions: Read the graph in each context. The horizontal axis is time t; the vertical axis is the stated quantity.

1.
$\text{Water}$ $\text{in}$ $\text{liters,}$ $\text{time}$ $\text{in}$ $\text{minutes.}$ $\text{Find}$ $\text{the}$ $\text{signed}$ $\text{rate}$ $\text{of}$ $\text{change.}$
2.
$\text{Height}$ $\text{in}$ $\text{cm,}$ $\text{time}$ $\text{in}$ $\text{weeks.}$ $\text{Find}$ $\text{the}$ $\text{rate}$ $\text{of}$ $\text{growth.}$
3.
$\text{Savings}$ $\text{in}$ $\text{dollars,}$ $\text{time}$ $\text{in}$ $\text{weeks.}$ $\text{Write}$ $\text{the}$ $\text{function}$ $\text{rule.}$
4.
$\text{Water}$ $\text{in}$ $\text{liters,}$ $\text{time}$ $\text{in}$ $\text{minutes.}$ $\text{Write}$ $\text{the}$ $\text{function}$ $\text{rule.}$
5.
$\text{Distance}$ $\text{from}$ $\text{home}$ $\text{in}$ $\text{km,}$ $\text{time}$ $\text{in}$ $\text{hours.}$ $\text{Find}$ $\text{the}$ $\text{speed}$ $\text{on}$ $\text{the}$ $\text{return}$ $\text{journey.}$
6.
$\text{Temperature}$ $\text{in}$ $\text{degrees}$ $\text{Celsius,}$ $\text{time}$ $\text{in}$ $\text{minutes.}$ $\text{Find}$ $\text{the}$ $\text{rate}$ $\text{from}$ $\text{4}$ $\text{to}$ $\text{6}$ $\text{minutes.}$
7.
$\text{Distance}$ $\text{from}$ $\text{home}$ $\text{in}$ $\text{km,}$ $\text{time}$ $\text{in}$ $\text{hours.}$ $\text{How}$ $\text{far}$ $\text{does}$ $\text{the}$ $\text{person}$ $\text{travel}$ $\text{in}$ $\text{total?}$
8.
$\text{Temperature}$ $\text{in}$ $\text{degrees}$ $\text{Celsius,}$ $\text{time}$ $\text{in}$ $\text{minutes.}$ $\text{For}$ $\text{how}$ $\text{long}$ $\text{does}$ $\text{it}$ $\text{stay}$ $\text{at}$ $\text{its}$ $\text{maximum?}$

Answer Key

Level 3

1. $-2\text{ L/min}$
2. $1\text{ cm/week}$
3. $y=5t+10$
4. $y=8-2t$
5. $2\text{ km/h}$
6. $-5^\circ\text{C/min}$
7. $8\text{ km}$
8. $2\text{ min}$

Grade 8 Algebra: Graphing Functions

Name: ______________________Date: ____________Score: ____ / 8

Level 1

Linear functions

Directions: Plot at least three points and draw each function on the grid. Each grid step is one unit.

1.
$y = 1x$
2.
$y = 1x + 2$
3.
$y = 2x$
4.
$y = 2x - 1$
5.
$y = 3$
6.
$y = 1x - 2$
7.
$y = -1x$
8.
$y = -1x + 2$

Answer Key

Level 1

1. $\text{Through }(0, 0), (2, 2)$
2. $\text{Through }(0, 2), (2, 4)$
3. $\text{Through }(0, 0), (2, 4)$
4. $\text{Through }(0, -1), (2, 3)$
5. $\text{Through }(0, 3), (2, 3)$
6. $\text{Through }(0, -2), (2, 0)$
7. $\text{Through }(0, 0), (2, -2)$
8. $\text{Through }(0, 2), (2, 0)$

Grade 8 Algebra: Graphing Functions

Name: ______________________Date: ____________Score: ____ / 8

Level 2

Negative and fractional slopes

Directions: Plot at least three points and draw each function on the grid. Each grid step is one unit.

1.
$y = -2x + 1$
2.
$y = 0.5x$
3.
$y = -0.5x + 2$
4.
$y = 1.5x - 1$
5.
$y = -1x - 2$
6.
$y = 0.5x - 3$
7.
$y = -1.5x + 1$
8.
$y = 2x - 3$

Answer Key

Level 2

1. $\text{Through }(0, 1), (2, -3)$
2. $\text{Through }(0, 0), (2, 1)$
3. $\text{Through }(0, 2), (2, 1)$
4. $\text{Through }(0, -1), (2, 2)$
5. $\text{Through }(0, -2), (2, -4)$
6. $\text{Through }(0, -3), (2, -2)$
7. $\text{Through }(0, 1), (2, -2)$
8. $\text{Through }(0, -3), (2, 1)$

Grade 8 Algebra: Graphing Functions

Name: ______________________Date: ____________Score: ____ / 8

Level 3

Linear and nonlinear functions

Directions: Plot at least three points and draw each function on the grid. Each grid step is one unit.

1.
$y=x^2$
2.
$y=|x|$
3.
$y=x^2-2$
4.
$y=-x^2+3$
5.
$y = -0.5x + 1$
6.
$y=|x|-2$
7.
$y=(x-1)^2$
8.
$y = 1x + 3$

Answer Key

Level 3

1. $\text{Points: }(-1, 1), (0, 0), (1, 1)$
2. $\text{Points: }(-1, 1), (0, 0), (1, 1)$
3. $\text{Points: }(-1, -1), (0, -2), (1, -1)$
4. $\text{Points: }(-1, 2), (0, 3), (1, 2)$
5. $\text{Through }(0, 1), (2, 0)$
6. $\text{Points: }(-1, -1), (0, -2), (1, -1)$
7. $\text{Points: }(-1, 4), (0, 1), (1, 0)$
8. $\text{Through }(0, 3), (2, 5)$