Lesson Worksheet: Cubic Functions and Their Graphs Mathematics

In this worksheet, we will practice graphing cubic functions, writing their rules from their graphs, and identifying their features.

Q1:

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

  • A(d)
  • B(a)
  • C(c)
  • D(b)

Q2:

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

Q3:

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(−1,−1)
  • B(−2,−2)
  • C(−2,2)
  • D(0,0)
  • EIt does not exist.

Q4:

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

  • A
  • B
  • C
  • D
  • E

Q5:

Ethan 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?

Q6:

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

Q7:

Select the equation of this curve.

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

Q8:

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

  • A(d)
  • B(b)
  • C(a)
  • D(c)

Q9:

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

Q10:

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

  • AA
  • BC
  • CD
  • DB

Q11:

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

Q12:

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

  • AB
  • BA
  • CD
  • DC

Q13:

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

  • AC
  • BD
  • CB
  • DA

Q14:

Which equation matches the graph?

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

Q15:

Which of the following is a set of points that lie on the curve 𝑦=𝑥+1?

  • A{(−1,0),(0,1),(1,2)}
  • B{(−1,0),(0,1),(1,3)}
  • C{(−1,−1),(0,0),(1,1)}
  • D{(−1,2),(0,3),(1,4)}
  • E{(−1,1),(0,2),(1,3)}

Q16:

If 𝑓(𝑥)=𝑥 is changed to 𝑦=(𝑥+1)+5, how is the graph transformed?

  • AHorizontally shifted left by 5 and vertically shifted down by 1
  • BHorizontally shifted left by 5 and vertically shifted up by 1
  • CHorizontally shifted left by 1 and vertically shifted up by 5
  • DHorizontally shifted right by 1 and vertically shifted up by 5
  • EHorizontally shifted right by 1 and vertically shifted down by 5

Q17:

If 𝑓(𝑥)=𝑥 is changed to 𝑓(𝑥)=(𝑥−1)+5, how is the graph transformed?

  • AHorizontally shifted left by 5 and vertically shifted up by 1
  • BHorizontally shifted left by 5 and vertically shifted down by 1
  • CHorizontally shifted right by 1 and vertically shifted down by 5
  • DHorizontally shifted left by 1 and vertically shifted up by 5
  • EHorizontally shifted right by 1 and vertically shifted up by 5

Q18:

If 𝑓(𝑥)=𝑥 is changed to 𝑦=−2(𝑥+1), how is the graph transformed?

  • AStretched in the 𝑦-direction by 2, reflected in the 𝑥-axis, and shifted left by 1
  • BStretched in the 𝑦-direction by a factor of 2, reflected in the 𝑥-axis, and shifted left by 1
  • CStretched in the 𝑦-direction by 2, reflected in the 𝑦-axis, and shifted left by 1
  • DStretched in the 𝑦-direction by 2, reflected in the 𝑥-axis, and shifted right by 1
  • EShrunk in the 𝑦-direction by 2, reflected in the 𝑦-axis, and shifted left by 1

Q19:

Which equation matches the red graph?

  • A𝑦=𝑥
  • B𝑦=0.5𝑥
  • C𝑦=0.25𝑥
  • D𝑦=2𝑥
  • E𝑦=4𝑥

Q20:

Which equation matches the green graph?

  • A𝑦=(𝑥+2)
  • B𝑦=𝑥
  • C𝑦=(𝑥−4)
  • D𝑦=(𝑥+4)
  • E𝑦=(𝑥−2)

Q21:

The graph of 𝑓(𝑥)=𝑥 is transformed so that its point of symmetry is (−1,5).

Which of the following could be the equation of the transformed graph?

  • A𝑓(𝑥)=(𝑥+1)+5
  • B𝑓(𝑥)=(𝑥−1)+5
  • C𝑓(𝑥)=(𝑥+1)−5
  • D𝑓(𝑥)=(𝑥+5)+1
  • E𝑓(𝑥)=(𝑥−5)−1

Q22:

Which equation matches the red graph?

  • A𝑦=𝑥+2
  • B𝑦=𝑥
  • C𝑦=𝑥−4
  • D𝑦=𝑥+4
  • E𝑦=𝑥−2

Q23:

The graph of 𝑓(𝑥)=𝑥 has been transformed so that its point of symmetry is (1,5). Which of the following could be the equation of the transformed graph?

  • A𝑓(𝑥)=(𝑥+5)−1
  • B𝑓(𝑥)=(𝑥−1)+5
  • C𝑓(𝑥)=(𝑥−5)+1
  • D𝑓(𝑥)=(𝑥−1)−5
  • E𝑓(𝑥)=(𝑥+1)+5

Q24:

If 𝑓(𝑥)=𝑥 is changed to 𝑦=0.1(𝑥−10), how is the graph transformed?

  • AStretched by a factor of 10 in the 𝑦-direction and shifted right by 0.1
  • BStretched by a factor of 0.1 in the 𝑦-direction and shifted right by 10
  • CStretched by a factor of 0.1 in the 𝑦-direction and shifted left by 10
  • DStretched by a factor of 0.1 in the 𝑦-direction and shifted right by 10
  • EStretched by a factor of 10 in the 𝑦-direction and shifted left by 0.1

Q25:

The graph of 𝑓(𝑥)=𝑥 has been transformed so that its point of symmetry is (−1,−5). Which of the following could be the equation of the transformed graph?

  • A𝑓(𝑥)=(𝑥+1)−5
  • B𝑓(𝑥)=(𝑥+1)+5
  • C𝑓(𝑥)=(𝑥−1)−5
  • D𝑓(𝑥)=(𝑥+5)−1
  • E𝑓(𝑥)=(𝑥−5)+1

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