Worksheet: Graphing Cubic Functions

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In this worksheet, we will practice graphing cubic functions and writing their rule from the given graph.

Q1:

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

  • A(d)
  • B(a)
  • C(c)
  • D(b)

Q2:

Find the equation for the graph.

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

Q3:

Find the function shown in the figure.

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

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 I t d o e s n o t e x i s t .
  • B ( − 2 , − 2 )
  • C ( − 2 , 2 )
  • D ( 0 , 0 )
  • E ( − 1 , − 1 )

Q5:

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

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

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

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

Q6:

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

  • A
  • B
  • C
  • D
  • E

Q7:

David starts with 𝑓(𝑥)=𝑥−1 and has a graph ()a that satisfies 𝑓(1)=0. He sees that the function 𝑔(𝑥)=(𝑥−𝑘)−(1−𝑘) will have a graph that also has 𝑥-intercept 1.

What is the value of 𝑘 that gives the graph in ()b?

Q8:

Which equation matches the graph?

  • A 𝑦 = 1 2 ( 𝑥 − 1 ) + 4
  • B 𝑦 = 1 3 ( 𝑥 − 1 ) + 4
  • C 𝑦 = 3 ( 𝑥 − 1 ) + 4
  • D 𝑦 = 2 ( 𝑥 − 1 ) + 4
  • E 𝑦 = ( 𝑥 − 1 ) + 4

Q9:

Select the equation of this curve.

  • A 𝑦 = − 2 𝑥 − 3
  • B 𝑦 = 2 𝑥 + 3
  • C 𝑦 = 𝑥 − 3
  • D 𝑦 = 𝑥 + 3
  • E 𝑦 = − 𝑥 − 3

Q10:

Which graph represents the function 𝑦=−2.5𝑥+3?

  • A(d)
  • B(b)
  • C(a)
  • D(c)

Q11:

Which equation matches the graph?

  • A 𝑦 = 2 5 ( 𝑥 − 1 ) + 2
  • B 𝑦 = − ( 𝑥 − 1 ) + 2
  • C 𝑦 = − 2 5 ( 𝑥 + 1 ) + 2
  • D 𝑦 = ( 𝑥 − 1 ) + 2
  • E 𝑦 = − 2 5 ( 𝑥 − 1 ) + 2

Q12:

Which of the graphs matches the equation 𝑦=14(𝑥−3)−1?

  • AA
  • BC
  • CD
  • DB

Q13:

Which equation matches the graph?

  • A 𝑦 = − 1 3 ( 𝑥 − 3 ) + 2
  • B 𝑦 = 1 3 ( 𝑥 − 3 ) + 2
  • C 𝑦 = 1 3 ( 𝑥 + 3 ) + 2
  • D 𝑦 = − 1 3 ( 𝑥 + 3 ) + 2
  • E 𝑦 = 1 3 ( 𝑥 + 2 ) − 3

Q14:

Which of the graphs matches the equation 𝑦=−2(𝑥+3)+2?

  • AB
  • BA
  • CD
  • DC

Q15:

Which of the graphs matches the equation 𝑦=2(𝑥+2)+3?

  • AC
  • BD
  • CB
  • DA

Q16:

Which equation matches the graph?