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Worksheet: Linear and Nonlinear Functions

In this worksheet, we will practice determining whether a function is linear or nonlinear.

Q1:

Determine whether the given figure represents a linear or nonlinear function.

  • Aa nonlinear function
  • Ba linear function

Q2:

Determine whether the given figure represents a linear or nonlinear function.

  • Aa nonlinear function
  • Ba linear function

Q3:

Which of the following equations represents a nonlinear function?

  • A 𝑦 = π‘₯ 2
  • B 𝑦 = 5 π‘₯ + 6
  • C 𝑦 = 5 ( π‘₯ βˆ’ 3 )
  • D 9 π‘₯ 𝑦 = 4

Q4:

Determine whether the table below represents a linear or nonlinear function.

x 3 6 9 12
y 32 25 18 11
  • Alinear function
  • Bnonlinear function

Q5:

Which of these functions is not linear?

  • A 𝑦 + 3 = 5 π‘₯
  • B 𝑦 = 3 π‘₯ + 5
  • C 3 π‘₯ βˆ’ 𝑦 = 5
  • D 𝑦 = 5 π‘₯ 3

Q6:

Does the shown figure represent a linear function?

  • Ano
  • Byes

Q7:

Is this a graph of a linear or a nonlinear function?

  • Alinear function
  • Bnonlinear function

Q8:

Determine whether the given table represents a linear or nonlinear function.

π‘₯ -value βˆ’ 1 0 1 2
𝑦 -value 5 2 5 14
  • A a nonlinear function
  • B a linear function

Q9:

Determine whether the function 𝑦 = π‘₯ + 8 3 is a linear or nonlinear function.

  • Aa nonlinear function
  • Ba linear function

Q10:

Determine whether the given table of values must be from a nonlinear function, or could be from a linear function.

π‘₯ -value 0 2 4 6
𝑦 -value 1 3 9 19
  • AIt must be from a nonlinear function.
  • BIt could be from a linear function.

Q11:

Determine whether the given figure represents a linear or nonlinear function.

  • Aa nonlinear function
  • Ba linear function

Q12:

Is any cubic function a nonlinear function?

  • Ayes
  • Bno

Q13:

Is 𝑦 = 2 π‘₯ + 8 a linear function?

  • Ayes
  • Bno

Q14:

Could the following table of values be from a linear function?

π‘₯ -value βˆ’ 1 0 1 2 3
𝑦 -value 7 5 3 1 βˆ’ 1
  • Ayes
  • Bno

Q15:

Determine whether the given table of values must be from a nonlinear function, or could be from a linear function.

π‘₯ -value βˆ’ 1 0 1 2
𝑦 -value 5 2 5 14
  • Aa nonlinear function
  • Ba linear function

Q16:

Determine whether the function 𝑦 = π‘₯ + 2 π‘₯ + 1 2 is a linear or nonlinear function.

  • Aa nonlinear function
  • Ba linear function

Q17:

Determine whether the given figure represents a linear or nonlinear function.

  • A a nonlinear function
  • B a linear function

Q18:

The table below shows the measures of the heights and bases of several triangles. Are the heights of the triangles a linear function of the bases?

Base (in) 2.4 4.3 5.3 6.3
Height (in) 8.5 7.2 5.1 2.2
  • Ano
  • Byes

Q19:

Does the equation 𝑦 = βˆ’ 8 π‘₯ represent a linear or a nonlinear function?

  • Alinear function
  • Bnonlinear function

Q20:

After graphing the function 2 𝑦 = 2 π‘₯ + 2 π‘₯ π‘₯ + π‘₯ βˆ’ 8 π‘₯ 5 2 4 , determine whether it is a linear or a nonlinear function.

  • AIt is a linear function.
  • BIt is a nonlinear function.

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