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Comparing Functions: Classroom Packet

Grade 8 Algebra: Comparing Functions

Name: ______________________Date: ____________Score: ____ / 8

Level 1

Greater rate of change

  1. 1. Which has the greater rate of change:
    A:y=3x+1B:x012y246\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. 2. Which has the greater rate of change:
    A:y=2x+5B:x012y159\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. 3. Which has the greater rate of change:
    A:y=−x+4B:x012y024\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. 4. Which has the greater rate of change:
    A:y=5xB:x024y31323\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. 5. Which has the greater rate of change:
    A:y=x+6B:x123y369\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. 6. Which has the greater rate of change:
    A:y=4x−2B:x012y71013\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. 7. Which has the greater rate of change:
    A:y=12xB:x048y012\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. 8. Which has the greater rate of change:
    A:y=6x+1B:x234y81420\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. 1. A (3>2)\text{A } (3 > 2)
  2. 2. B (4>2)\text{B } (4 > 2)
  3. 3. B (2>−1)\text{B } (2 > -1)
  4. 4. Same (5)\text{Same } (5)
  5. 5. B (3>1)\text{B } (3 > 1)
  6. 6. A (4>3)\text{A } (4 > 3)
  7. 7. A (12>14)\text{A } (\tfrac12 > \tfrac14)
  8. 8. Same (6)\text{Same } (6)

Grade 8 Algebra: Comparing Functions

Name: ______________________Date: ____________Score: ____ / 8

Level 2

Greater initial value

  1. 1. Which has the greater initial value:
    A:y=2x+7B:x012y468\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. 2. Which has the greater initial value:
    A:y=−3x+2B:x012y52−1\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. 3. Which has the greater initial value:
    A:y=x−4B:x123y012\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. 4. Which has the greater initial value:
    A:y=4x+3B:x123y579\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. 5. Which has the greater initial value:
    A:y=12x+6B:x246y91011\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. 6. Which has the greater initial value:
    A:y=−2x+10B:x123y111417\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. 7. Which has the greater initial value:
    A:y=5xB:x123y210\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. 8. Which has the greater initial value:
    A:y=3x−1B:x−101y−6−22\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. 1. A (7>4)\text{A } (7 > 4)
  2. 2. B (5>2)\text{B } (5 > 2)
  3. 3. B (−1>−4)\text{B } (-1 > -4)
  4. 4. Same (3)\text{Same } (3)
  5. 5. B (8>6)\text{B } (8 > 6)
  6. 6. A (10>8)\text{A } (10 > 8)
  7. 7. B (3>0)\text{B } (3 > 0)
  8. 8. A (−1>−2)\text{A } (-1 > -2)

Grade 8 Algebra: Comparing Functions

Name: ______________________Date: ____________Score: ____ / 8

Level 3

Real-life comparisons

  1. 1. x{x} = hours, y{y} = miles. Which car is faster:
    A:y=55xB:x123y60120180\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. 2. x{x} = months, y{y} = total cost in dollars. Which gym has the lower joining fee:
    A:y=30x+50B:x123y65100135\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. 3. x{x} = months, y{y} = total cost in dollars. Which gym costs less per month:
    A:y=30x+50B:x123y65100135\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. 4. x{x} = weeks, y{y} = dollars saved. Who saves more each week:
    A:y=15x+20B:x024y406488\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. 5. x{x} = minutes, y{y} = liters left. Which tank drains faster:
    A:y=−4x+100B:x0510y805530\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. 6. x{x} = minutes, y{y} = liters left. Which tank starts with more water:
    A:y=−4x+100B:x0510y805530\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. 7. x{x} = weeks, y{y} = height in cm. Which plant grows faster:
    A:y=0.5x+12B:(2,10), (6,13)\begin{array}{ll} \textbf{A:} & y = 0.5x + 12 \\[14pt] \textbf{B:} & (2, 10),\ (6, 13) \end{array}
  8. 8. x{x} = texts, y{y} = cost in dollars. When do the plans cost the same:
    A:y=0.1x+20B:x0100200y104070\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. 1. B (60 mph)\text{B } (60\text{ mph})
  2. 2. B ($30)\text{B } (\$30)
  3. 3. A ($30<$35)\text{A } (\$30 < \$35)
  4. 4. A ($15>$12)\text{A } (\$15 > \$12)
  5. 5. B (5 L/min)\text{B } (5\text{ L/min})
  6. 6. A (100 L)\text{A } (100\text{ L})
  7. 7. B (0.75>0.5)\text{B } (0.75 > 0.5)
  8. 8. 50 texts, $2550\text{ texts, }\$25