Worksheet: Graphing Cubic Functions

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In this worksheet, we will practice graphing cubic functions given in vertex form.

Q1:

Which of the following graphs represents 𝑓 ( 𝑥 ) = 2 − ( 𝑥 − 5 ) 3 ?

  • A(c)
  • B(a)
  • C(d)
  • D(b)

Q2:

Find the equation for the graph.

  • A 𝑓 ( 𝑥 ) = 𝑥 2
  • B 𝑓 ( 𝑥 ) = √ 𝑥
  • C 𝑓 ( 𝑥 ) = 1 𝑥
  • D 𝑓 ( 𝑥 ) = 𝑥 3

Q3:

Find the function shown in the figure.

  • A 𝑓 ( 𝑥 ) = ( 𝑥 − 4 ) + 4 3
  • B 𝑓 ( 𝑥 ) = ( 𝑥 + 4 ) − 4 3
  • C 𝑓 ( 𝑥 ) = − ( 𝑥 − 4 ) + 4 3
  • D 𝑓 ( 𝑥 ) = − ( 𝑥 + 4 ) − 4 3

Q4:

Consider the graph of the function 𝑦 = ( 𝑥 + 2 ) − 2 .

Write down the coordinates of the point of symmetry of the graph, if it exists.

  • A
  • B ( 0 , 0 )
  • C ( − 2 , 2 )
  • D ( − 2 , − 2 )
  • E ( − 1 , − 1 )

Q5:

The given figure shows the graph of 𝑓 ( 𝑥 ) = 𝑥 − 4 𝑥 + 1 3 2 .

Use the graph to determine the number of solutions to the equation 𝑥 = 4 𝑥 − 1 3 2 .

Use the graph to determine the intervals in which the solutions to 𝑥 = 4 𝑥 − 1 3 2 lie.

  • A − 1 < 𝑥 < 0 , 0 < 𝑥 < 1 , and 3 < 𝑥 < 4
  • B − 0 . 5 < 𝑥 < 0 , 0 < 𝑥 < 2 , and 3 < 𝑥 < 4
  • C − 1 < 𝑥 < 0 , 0 < 𝑥 < 1 , and 4 < 𝑥 < 5
  • D − 1 < 𝑥 < − 0 . 5 , − 0 . 5 < 𝑥 < 0 , and 3 < 𝑥 < 4
  • E − 0 . 5 < 𝑥 < 0 , 0 < 𝑥 < 0 . 5 , and 4 < 𝑥 < 5

Q6:

Which of the following is the graph of 𝑓 ( 𝑥 ) = − ( 𝑥 − 2 ) 3 ?

  • A
  • B
  • C
  • D
  • E

Q7:

Karim starts with and has a graph that satisfies . He sees that the function will have a graph that also has -intercept 1.

What is the value of that gives the graph in ?

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