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.

  • A𝑓(𝑥)=𝑥
  • B𝑓(𝑥)=√𝑥
  • C𝑓(𝑥)=𝑥
  • D𝑓(𝑥)=1𝑥

Q3:

Find the function shown in the figure.

  • A𝑓(𝑥)=−(𝑥−4)+4
  • B𝑓(𝑥)=(𝑥−4)+4
  • C𝑓(𝑥)=−(𝑥+4)−4
  • D𝑓(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.

  • AItdoesnotexist.
  • 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?

  • A𝑦=12(𝑥−1)+4
  • B𝑦=13(𝑥−1)+4
  • C𝑦=3(𝑥−1)+4
  • D𝑦=2(𝑥−1)+4
  • E𝑦=(𝑥−1)+4

Q9:

Select the equation of this curve.

  • A𝑦=−2𝑥−3
  • B𝑦=2𝑥+3
  • C𝑦=𝑥−3
  • D𝑦=𝑥+3
  • E𝑦=−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?

  • A𝑦=25(𝑥−1)+2
  • B𝑦=−(𝑥−1)+2
  • C𝑦=−25(𝑥+1)+2
  • D𝑦=(𝑥−1)+2
  • E𝑦=−25(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?

  • A𝑦=−13(𝑥−3)+2
  • B𝑦=13(𝑥−3)+2
  • C𝑦=13(𝑥+3)+2
  • D𝑦=−13(𝑥+3)+2
  • E𝑦=13(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?

  • A𝑦=(𝑥−2)−1
  • B𝑦=(𝑥−2)+1
  • C𝑦=(𝑥+2)−1
  • D𝑦=(𝑥+2)+1

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