Lesson Worksheet: Graphing Linear Functions Mathematics

In this worksheet, we will practice graphing linear functions.

Q1:

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

  • Aa nonlinear function
  • Ba linear function

Q2:

Consider the function 𝑓, 𝑓(𝑥)=2𝑥4. Its graph is given in the following diagram.

At which point does the graph of 𝑓 intersect the 𝑥-axis?

  • A(2,4)
  • B(0,4)
  • C(2,0)
  • D(2,0)
  • E(0,4)

At which point does the graph of 𝑓 intersect the 𝑦-axis?

  • A(0,4)
  • B(2,0)
  • C(0,4)
  • D(2,0)
  • E(2,4)

Q3:

If the linear function given by the rule 𝑓(𝑥)=3𝑥+12 is represented by a straight line, at which point does it intersect the 𝑦-axis?

  • A(0,12)
  • B(12,0)
  • C(4,0)
  • D(4,0)
  • E(0,12)

Q4:

By making a table of values, determine which of the following is the function represented by the graph shown.

  • A𝑓(𝑥)=3𝑥+1
  • B𝑓(𝑥)=3𝑥1
  • C𝑓(𝑥)=3𝑥+1
  • D𝑓(𝑥)=3𝑥1
  • E𝑓(𝑥)=13𝑥1

Q5:

Let us consider the function 𝑓(𝑥)=8𝑥11.

Fill in the table.

𝑥−101
𝑦=𝑓(𝑥)
  • A
    𝑥−101
    𝑦=𝑓(𝑥)−19−11−3
  • B
    𝑥−101
    𝑦=𝑓(𝑥)−3−113
  • C
    𝑥−101
    𝑦=𝑓(𝑥)−1983
  • D
    𝑥−101
    𝑦=𝑓(𝑥)3−11−3
  • E
    𝑥−101
    𝑦=𝑓(𝑥)30−3

Identify the three points that lie on the line 𝑦=8𝑥11.

  • A𝐴, 𝐶, 𝐸
  • B𝐼, 𝐻, 𝐺
  • C𝐴, 𝐶, 𝐷
  • D𝐹, 𝐻, 𝐽
  • E𝐵, 𝐶, 𝐷

Q6:

Identify which of the graphs represents the function 𝑓(𝑥)=12.

  • A𝐸
  • B𝐵
  • C𝐷
  • D𝐴
  • E𝐶

Q7:

Consider the linear function 𝑓(𝑥)=52𝑥.

We can draw a straight line to represent this function. Complete the table to find the coordinates of points on the line.

𝑥−2−1012
𝑓(𝑥)
  • A9, 7, 6, 3, 1
  • B9, 7, 5, 3, 1
  • C1, 3, 5, 7, 9
  • D9, 7, 5, 3, 2

Which of the following is the graph of the function?

  • A
  • B
  • C
  • D

Which of these points is not on the line?

  • A(4,3)
  • B(3,11)
  • C(4,13)
  • D(3,1)
  • E(6,6)

Q8:

By making a table of values, determine which of the following is the function represented by the graph shown.

  • A𝑓(𝑥)=4𝑥
  • B𝑓(𝑥)=4𝑥+1
  • C𝑓(𝑥)=4𝑥1
  • D𝑓(𝑥)=4𝑥+1
  • E𝑓(𝑥)=4𝑥

Q9:

The following table represents a linear function.

𝑥0123
𝑓(𝑥)13𝑎𝑏

Which of the following graphs represents this line?

  • A
  • B
  • C
  • D
  • E

Find the values of 𝑎 and 𝑏.

  • A𝑎=5, 𝑏=7
  • B𝑎=5, 𝑏=7
  • C𝑎=3, 𝑏=5
  • D𝑎=3.5, 𝑏=5.5
  • E𝑎=3.5, 𝑏=5.5

Write the equation of the straight line in the form 𝑓(𝑥)=𝑚𝑥+𝑐.

  • A𝑓(𝑥)=2𝑥+0.5
  • B𝑓(𝑥)=2𝑥+1
  • C𝑓(𝑥)=2𝑥0.5
  • D𝑓(𝑥)=2𝑥1
  • E𝑓(𝑥)=2𝑥+1

Q10:

Anthony wants to draw the graph of the linear function 𝑓(𝑥)=3𝑥4.

He plotted the points with 𝑥-coordinates 0, 1, 2, 3, and 4 but made one mistake.

Which point is incorrect?

  • AE
  • BB
  • CD
  • DA
  • EC

What are the correct coordinates of this point?

  • A(4,5)
  • B(4,4)
  • C(3,6)
  • D(3,4)
  • E(3,5)

This lesson includes 27 additional questions and 153 additional question variations for subscribers.

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