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Linear and Nonlinear Functions: Classroom Packet

Grade 8 Algebra: Linear and Nonlinear Functions

Name: ______________________Date: ____________Score: ____ / 8

Level 1

Equations

  1. 1. Linear or nonlinear:
    y=4x−1y = 4x - 1
  2. 2. Linear or nonlinear:
    y=x2y = x^2
  3. 3. Linear or nonlinear:
    y=−x+3y = -x + 3
  4. 4. Linear or nonlinear:
    y=1xy = \dfrac{1}{x}
  5. 5. Linear or nonlinear:
    y=7y = 7
  6. 6. Linear or nonlinear:
    y=x3y = x^3
  7. 7. Linear or nonlinear:
    y=12xy = \tfrac{1}{2}x
  8. 8. Linear or nonlinear:
    y=2xy = 2^x

Answer Key

Level 1

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

Grade 8 Algebra: Linear and Nonlinear Functions

Name: ______________________Date: ____________Score: ____ / 8

Level 2

Tables

  1. 1. Linear or nonlinear:
    x0123y1357\begin{array}{c|cccc} x & 0 & 1 & 2 & 3 \\ \hline y & 1 & 3 & 5 & 7 \end{array}
  2. 2. Linear or nonlinear:
    x0123y0149\begin{array}{c|cccc} x & 0 & 1 & 2 & 3 \\ \hline y & 0 & 1 & 4 & 9 \end{array}
  3. 3. Linear or nonlinear:
    x1234y10741\begin{array}{c|cccc} x & 1 & 2 & 3 & 4 \\ \hline y & 10 & 7 & 4 & 1 \end{array}
  4. 4. Linear or nonlinear:
    x1234y24816\begin{array}{c|cccc} x & 1 & 2 & 3 & 4 \\ \hline y & 2 & 4 & 8 & 16 \end{array}
  5. 5. Linear or nonlinear:
    x0246y5678\begin{array}{c|cccc} x & 0 & 2 & 4 & 6 \\ \hline y & 5 & 6 & 7 & 8 \end{array}
  6. 6. Linear or nonlinear:
    x−1012y1014\begin{array}{c|cccc} x & -1 & 0 & 1 & 2 \\ \hline y & 1 & 0 & 1 & 4 \end{array}
  7. 7. Linear or nonlinear:
    x2468y3333\begin{array}{c|cccc} x & 2 & 4 & 6 & 8 \\ \hline y & 3 & 3 & 3 & 3 \end{array}
  8. 8. Linear or nonlinear:
    x0134y24810\begin{array}{c|cccc} x & 0 & 1 & 3 & 4 \\ \hline y & 2 & 4 & 8 & 10 \end{array}

Answer Key

Level 2

  1. 1. Linear (+2)\text{Linear}\ (+2)
  2. 2. Nonlinear\text{Nonlinear}
  3. 3. Linear (−3)\text{Linear}\ (-3)
  4. 4. Nonlinear\text{Nonlinear}
  5. 5. Linear (12)\text{Linear}\ (\tfrac{1}{2})
  6. 6. Nonlinear\text{Nonlinear}
  7. 7. Linear (0)\text{Linear}\ (0)
  8. 8. Linear (2)\text{Linear}\ (2)

Grade 8 Algebra: Linear and Nonlinear Functions

Name: ______________________Date: ____________Score: ____ / 8

Level 3

Rewrite first

  1. 1. Linear or nonlinear:
    2x+y=62x + y = 6
  2. 2. Linear or nonlinear:
    y=x(x+1)y = x(x + 1)
  3. 3. Linear or nonlinear:
    y−3=2(x+1)y - 3 = 2(x + 1)
  4. 4. Linear or nonlinear:
    xy=12xy = 12
  5. 5. Linear or nonlinear:
    y=x+42y = \dfrac{x + 4}{2}
  6. 6. Linear or nonlinear:
    y=3x2−3x2+5xy = 3x^2 - 3x^2 + 5x
  7. 7. Linear or nonlinear:
    y=(x+2)2−x2y = (x + 2)^2 - x^2
  8. 8. Linear or nonlinear:
    y=6x+1y = \dfrac{6}{x} + 1

Answer Key

Level 3

  1. 1. Linear (y=−2x+6)\text{Linear}\ (y = -2x + 6)
  2. 2. Nonlinear (x2+x)\text{Nonlinear}\ (x^2 + x)
  3. 3. Linear (y=2x+5)\text{Linear}\ (y = 2x + 5)
  4. 4. Nonlinear\text{Nonlinear}
  5. 5. Linear (y=12x+2)\text{Linear}\ (y = \tfrac{1}{2}x + 2)
  6. 6. Linear (y=5x)\text{Linear}\ (y = 5x)
  7. 7. Linear (y=4x+4)\text{Linear}\ (y = 4x + 4)
  8. 8. Nonlinear\text{Nonlinear}