# 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

Q8:

Which graph represents the function ?    • A(d)
• B(b)
• C(a)
• D(c)

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