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

Q4:

Which of the following equations represents a nonlinear function?

• A
• B
• C
• D

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
• B
• C
• D

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

Q10:

Is a linear function?

• Ayes
• Bno

Q11:

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

 𝑥-value 𝑦-value −1 0 1 2 3 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 𝑦-value −1 0 1 2 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) Height (in) 2.4 4.3 5.3 6.3 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 , 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 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 represent a linear or a nonlinear function?

• Alinear function
• Bnonlinear function

Q19:

Determine whether the function 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 to calculate the gross profit that the store makes, in dollars, when it sells 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 Ticket Sales 1 2 3 \$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) Distance (mi) 2 4 6 8 130 260 390 520
• AYes
• BNo

Q24:

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

• A, ,
• B, ,
• C, ,
• D, ,
• E, ,

Q25:

Consider the function , where is a positive integer and is a constant. What value of would make the function linear?

• A
• B
• C
• D
• E