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.

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

Q4:

Which of the following equations represents a nonlinear function?

  • A 𝑦 = 5 ( 𝑥 3 )
  • B 9 𝑥 𝑦 = 4
  • C 𝑦 = 5 𝑥 + 6
  • D 𝑦 = 𝑥 2

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?

  • A 𝑦 = 3 𝑥 + 5
  • B 𝑦 + 3 = 5 𝑥
  • C 3 𝑥 𝑦 = 5
  • D 𝑦 = 5 𝑥

Q7:

Does the shown figure represent a linear function?

  • Ayes
  • Bno

Q8:

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

𝑥 -value 1 0 1 2
𝑦 -value 5 2 5 14
  • 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 -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.

Q10:

Is 𝑦=2𝑥+8 a linear function?

  • Ayes
  • Bno

Q11:

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

𝑥 -value 1 0 1 2 3
𝑦 -value 7 5 3 1 1
  • Ano
  • Byes

Q12:

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

𝑥 -value 1 0 1 2
𝑦 -value 5 2 5 14
  • 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) 2.4 4.3 5.3 6.3
Height (in) 8.5 7.2 5.1 2.2
  • 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 Sold 1 2 3
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) 2 4 6 8
Distance (mi) 130 260 390 520
  • 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 , 1 4 )
  • D ( 2 , 3 ) , ( 3 , 2 4 ) , ( 4 , 6 1 )
  • E ( 2 , 4 ) , ( 3 , 9 ) , ( 4 , 1 6 )

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?

  • A 𝑛 = 2
  • B 𝑛 = 3
  • C 𝑛 = 1 2
  • D 𝑛 = 1
  • E 𝑛 = 0

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