# 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 ?

- A(d)
- B(a)
- C(c)
- D(b)

**Q2: **

Find the function shown in the figure.

- A
- B
- C
- D

**Q3: **

Consider the graph of the function .

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

- A
- B
- C
- D
- EIt does not exist.

**Q4: **

Which of the following is the graph of ?

- A
- B
- C
- D
- E

**Q5: **

Ethan 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 ?

**Q6: **

Which equation matches the graph?

- A
- B
- C
- D
- E

**Q7: **

Select the equation of this curve.

- A
- B
- C
- D
- E

**Q9: **

Which equation matches the graph?

- A
- B
- C
- D
- E

**Q10: **

Which of the graphs matches the equation ?

- AA
- BC
- CD
- DB

**Q11: **

Which equation matches the graph?

- A
- B
- C
- D
- E

**Q12: **

Which of the graphs matches the equation ?

- AB
- BA
- CD
- DC

**Q13: **

Which of the graphs matches the equation ?

- AC
- BD
- CB
- DA

**Q14: **

Which equation matches the graph?

- A
- B
- C
- D

**Q15: **

Which of the following is a set of points that lie on the curve ?

- A
- B
- C
- D
- E

**Q16: **

If is changed to , 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 is changed to , 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 is changed to , how is the graph transformed?

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

**Q19: **

Which equation matches the red graph?

- A
- B
- C
- D
- E

**Q20: **

Which equation matches the green graph?

- A
- B
- C
- D
- E

**Q21: **

The graph of is transformed so that its point of symmetry is .

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

- A
- B
- C
- D
- E

**Q22: **

Which equation matches the red graph?

- A
- B
- C
- D
- E

**Q23: **

The graph of has been transformed so that its point of symmetry is . Which of the following could be the equation of the transformed graph?

- A
- B
- C
- D
- E

**Q24: **

If is changed to , how is the graph transformed?

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

**Q25: **

The graph of has been transformed so that its point of symmetry is . Which of the following could be the equation of the transformed graph?

- A
- B
- C
- D
- E