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 linear function
  • Ba nonlinear function

Q2:

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

  • Aa nonlinear function
  • Ba linear function

Q3:

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

x36912
y32251811
  • Alinear function
  • Bnonlinear function

Q4:

Which of the following equations represents a nonlinear function?

  • A𝑦=5(𝑥3)
  • B9𝑥𝑦=4
  • C𝑦=5𝑥+6
  • D𝑦=𝑥2

Q5:

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

  • Aa nonlinear function
  • Ba linear function

Q6:

Which of these functions is not linear?

  • A𝑦=3𝑥+5
  • B𝑦+3=5𝑥
  • C3𝑥𝑦=5
  • D𝑦=5𝑥

Q7:

Does the shown figure represent a linear function?

  • Ayes
  • Bno

Q8:

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

𝑥-value1012
𝑦-value52514
  • AA nonlinear function
  • BA linear function

Q9:

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

𝑥-value0246
𝑦-value13919
  • AIt must be from a nonlinear function.
  • BIt could be from a linear function.

Q10:

Is 𝑦=2𝑥+8 a linear function?

  • Ayes
  • Bno

Q11:

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

𝑥-value10123
𝑦-value75311
  • Ano
  • Byes

Q12:

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

𝑥-value1012
𝑦-value52514
  • Aa linear function
  • Ba nonlinear function

Q13:

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)2.44.35.36.3
Height (in)8.57.25.12.2
  • Ano
  • Byes

Q14:

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

  • Aa nonlinear function
  • Ba linear function

Q15:

After graphing the function 2𝑦=2𝑥+2𝑥𝑥+𝑥8𝑥, determine whether it is a linear or a nonlinear function.

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

Q16:

Determine whether the function 𝑦=𝑥+2𝑥+1 is a linear or nonlinear function.

  • Aa linear function
  • Ba nonlinear function

Q17:

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

  • Alinear function
  • Bnonlinear function

Q18:

Does the equation 𝑦=8𝑥 represent a linear or a nonlinear function?

  • Alinear function
  • Bnonlinear function

Q19:

Determine whether the function 𝑦=𝑥+8 is a linear or nonlinear function.

  • Aa nonlinear function
  • Ba linear function

Q20:

Is any cubic function a nonlinear function?

  • Ano
  • Byes

Q21:

A toy store uses the equation 𝑝=27𝑡65 to calculate the gross profit 𝑝 that the store makes, in dollars, when it sells 𝑡 toys. Is the gross profit a linear or nonlinear function of the number of toys sold?

  • Aa nonlinear function
  • Ba linear function

Q22:

The price of a ticket to a school dance is $8. Given the data in the table, do the ticket sales represent a linear function of the number of tickets sold?

Number of Tickets Sold123
Ticket Sales$8$16$24
  • Ayes
  • Bno

Q23:

A family went on a road trip. Given the information in the table, is the distance covered by the family a linear function of the number of hours they spent traveling?

Time (h)2468
Distance (mi)130260390520
  • AYes
  • BNo

Q24:

Which of the following sets of points could be from a linear function?

  • A(1,0), (0,2), (2,6)
  • B(2,8), (3,7), (1,1)
  • C(2,2), (3,7), (4,14)
  • D(2,3), (3,24), (4,61)
  • E(2,4), (3,9), (4,16)

Q25:

Consider the function 𝑓(𝑥)=𝑥+𝑏, where 𝑛 is a positive integer and 𝑏 is a constant. What value of 𝑛 would make the function linear?

  • A𝑛=2
  • B𝑛=3
  • C𝑛=12
  • D𝑛=1
  • E𝑛=0

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