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Linear and Nonlinear Graphs: Classroom Packet

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. 1.
    −5-5
    −4-4
    −3-3
    −2-2
    −1-1
    11
    22
    33
    44
    55
    −5-5
    −4-4
    −3-3
    −2-2
    −1-1
    11
    22
    33
    44
    55
    xx
    yy
  2. 2.
    −5-5
    −4-4
    −3-3
    −2-2
    −1-1
    11
    22
    33
    44
    55
    −5-5
    −4-4
    −3-3
    −2-2
    −1-1
    11
    22
    33
    44
    55
    xx
    yy
  3. 3.
    −5-5
    −4-4
    −3-3
    −2-2
    −1-1
    11
    22
    33
    44
    55
    −5-5
    −4-4
    −3-3
    −2-2
    −1-1
    11
    22
    33
    44
    55
    xx
    yy
  4. 4.
    −5-5
    −4-4
    −3-3
    −2-2
    −1-1
    11
    22
    33
    44
    55
    −5-5
    −4-4
    −3-3
    −2-2
    −1-1
    11
    22
    33
    44
    55
    xx
    yy
  5. 5.
    −5-5
    −4-4
    −3-3
    −2-2
    −1-1
    11
    22
    33
    44
    55
    −5-5
    −4-4
    −3-3
    −2-2
    −1-1
    11
    22
    33
    44
    55
    xx
    yy
  6. 6.
    −5-5
    −4-4
    −3-3
    −2-2
    −1-1
    11
    22
    33
    44
    55
    −5-5
    −4-4
    −3-3
    −2-2
    −1-1
    11
    22
    33
    44
    55
    xx
    yy
  7. 7.
    −5-5
    −4-4
    −3-3
    −2-2
    −1-1
    11
    22
    33
    44
    55
    −5-5
    −4-4
    −3-3
    −2-2
    −1-1
    11
    22
    33
    44
    55
    xx
    yy
  8. 8.
    −5-5
    −4-4
    −3-3
    −2-2
    −1-1
    11
    22
    33
    44
    55
    −5-5
    −4-4
    −3-3
    −2-2
    −1-1
    11
    22
    33
    44
    55
    xx
    yy

Answer Key

Level 1

  1. 1. Linear: straight line\text{Linear: straight line}
  2. 2. Nonlinear: not a straight line\text{Nonlinear: not a straight line}
  3. 3. Linear: straight line\text{Linear: straight line}
  4. 4. Nonlinear: not a straight line\text{Nonlinear: not a straight line}
  5. 5. Linear: straight line\text{Linear: straight line}
  6. 6. Nonlinear: not a straight line\text{Nonlinear: not a straight line}
  7. 7. Linear: straight line\text{Linear: straight line}
  8. 8. Nonlinear: not a straight line\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. 1.
    −5-5
    −4-4
    −3-3
    −2-2
    −1-1
    11
    22
    33
    44
    55
    −5-5
    −4-4
    −3-3
    −2-2
    −1-1
    11
    22
    33
    44
    55
    xx
    yy
  2. 2.
    −5-5
    −4-4
    −3-3
    −2-2
    −1-1
    11
    22
    33
    44
    55
    −5-5
    −4-4
    −3-3
    −2-2
    −1-1
    11
    22
    33
    44
    55
    xx
    yy
  3. 3.
    −5-5
    −4-4
    −3-3
    −2-2
    −1-1
    11
    22
    33
    44
    55
    −5-5
    −4-4
    −3-3
    −2-2
    −1-1
    11
    22
    33
    44
    55
    xx
    yy
  4. 4.
    −5-5
    −4-4
    −3-3
    −2-2
    −1-1
    11
    22
    33
    44
    55
    −5-5
    −4-4
    −3-3
    −2-2
    −1-1
    11
    22
    33
    44
    55
    xx
    yy
  5. 5.
    −5-5
    −4-4
    −3-3
    −2-2
    −1-1
    11
    22
    33
    44
    55
    −5-5
    −4-4
    −3-3
    −2-2
    −1-1
    11
    22
    33
    44
    55
    xx
    yy
  6. 6.
    −5-5
    −4-4
    −3-3
    −2-2
    −1-1
    11
    22
    33
    44
    55
    −5-5
    −4-4
    −3-3
    −2-2
    −1-1
    11
    22
    33
    44
    55
    xx
    yy
  7. 7.
    −5-5
    −4-4
    −3-3
    −2-2
    −1-1
    11
    22
    33
    44
    55
    −5-5
    −4-4
    −3-3
    −2-2
    −1-1
    11
    22
    33
    44
    55
    xx
    yy
  8. 8.
    −5-5
    −4-4
    −3-3
    −2-2
    −1-1
    11
    22
    33
    44
    55
    −5-5
    −4-4
    −3-3
    −2-2
    −1-1
    11
    22
    33
    44
    55
    xx
    yy

Answer Key

Level 2

  1. 1. Linear: straight line\text{Linear: straight line}
  2. 2. Nonlinear: not a straight line\text{Nonlinear: not a straight line}
  3. 3. Nonlinear: not a straight line\text{Nonlinear: not a straight line}
  4. 4. Linear: straight line\text{Linear: straight line}
  5. 5. Linear: straight line\text{Linear: straight line}
  6. 6. Nonlinear: not a straight line\text{Nonlinear: not a straight line}
  7. 7. Linear: straight line\text{Linear: straight line}
  8. 8. Nonlinear: not a straight line\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. 1.
    −5-5
    −4-4
    −3-3
    −2-2
    −1-1
    11
    22
    33
    44
    55
    −5-5
    −4-4
    −3-3
    −2-2
    −1-1
    11
    22
    33
    44
    55
    xx
    yy
  2. 2.
    −5-5
    −4-4
    −3-3
    −2-2
    −1-1
    11
    22
    33
    44
    55
    −5-5
    −4-4
    −3-3
    −2-2
    −1-1
    11
    22
    33
    44
    55
    xx
    yy
  3. 3.
    −5-5
    −4-4
    −3-3
    −2-2
    −1-1
    11
    22
    33
    44
    55
    −5-5
    −4-4
    −3-3
    −2-2
    −1-1
    11
    22
    33
    44
    55
    xx
    yy
  4. 4.
    −5-5
    −4-4
    −3-3
    −2-2
    −1-1
    11
    22
    33
    44
    55
    −5-5
    −4-4
    −3-3
    −2-2
    −1-1
    11
    22
    33
    44
    55
    xx
    yy
  5. 5.
    −5-5
    −4-4
    −3-3
    −2-2
    −1-1
    11
    22
    33
    44
    55
    −5-5
    −4-4
    −3-3
    −2-2
    −1-1
    11
    22
    33
    44
    55
    xx
    yy
  6. 6.
    −5-5
    −4-4
    −3-3
    −2-2
    −1-1
    11
    22
    33
    44
    55
    −5-5
    −4-4
    −3-3
    −2-2
    −1-1
    11
    22
    33
    44
    55
    xx
    yy
  7. 7.
    −5-5
    −4-4
    −3-3
    −2-2
    −1-1
    11
    22
    33
    44
    55
    −5-5
    −4-4
    −3-3
    −2-2
    −1-1
    11
    22
    33
    44
    55
    xx
    yy
  8. 8.
    −5-5
    −4-4
    −3-3
    −2-2
    −1-1
    11
    22
    33
    44
    55
    −5-5
    −4-4
    −3-3
    −2-2
    −1-1
    11
    22
    33
    44
    55
    xx
    yy

Answer Key

Level 3

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