Lesson Worksheet: Linear and Nonlinear Functions Mathematics • 8th Grade

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(π‘₯βˆ’3)
  • B9π‘₯𝑦=4
  • C𝑦=5π‘₯+6
  • D𝑦=π‘₯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?

  • A𝑦=3π‘₯+5
  • B𝑦+3=5π‘₯
  • C3π‘₯βˆ’π‘¦=5
  • D𝑦=5π‘₯

Q7:

Does the shown figure represent a linear function?

  • AYes
  • BNo

Q8:

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

π‘₯-valueβˆ’1012
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.

π‘₯-value0246
𝑦-value13919
  • AIt must be from a nonlinear function.
  • BIt could be from a linear function.

Q10:

Is 𝑦=2π‘₯+8 a linear function?

  • AYes
  • BNo

Q11:

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

π‘₯-valueβˆ’10123
𝑦-value7531βˆ’1
  • ANo
  • BYes

Q12:

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

π‘₯-valueβˆ’1012
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:

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

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

Q15:

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

  • Aa linear function
  • Ba nonlinear function

Q16:

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

  • Alinear function
  • Bnonlinear function

Q17:

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

  • Aa nonlinear function
  • Ba linear function

Q18:

Is any cubic function a nonlinear function?

  • ANo
  • BYes

Q19:

A toy store uses the equation 𝑝=27π‘‘βˆ’65 to calculate the gross profit 𝑝 that the store makes, in dollars, when it sells 𝑑 toys. Is the gross profit a linear or nonlinear function of the number of toys sold?

  • Aa nonlinear function
  • Ba linear function

Q20:

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

Q21:

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

Q22:

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

  • A(βˆ’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)

Q23:

Consider the function 𝑓(π‘₯)=π‘₯+π‘οŠ, 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

Q24:

Consider the following functions:

  1. 𝑦=2π‘₯+3π‘₯
  2. 2=π‘₯𝑦
  3. 𝑦=3π‘₯
  4. 𝑦+π‘₯=16
  5. 𝑦=π‘₯3

Identify which of the five functions are linear.

  • Ad, e, and b
  • Ba, b, and e
  • Cd and e
  • Db and c
  • Ea and b

Q25:

Which of the following is an equation?

  • A3π‘₯+6=βˆ’3
  • B5π‘₯+5
  • Cπ‘₯β‰₯5
  • D25+11

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