# Worksheet: Function Transformations: Translations

In this worksheet, we will practice identifying function transformations involving horizontal and vertical shifts.

Q1:

The graph of function is produced from that of by the following steps: a shift of 4 to the right, a dilation by a scale factor of , and a shift of 4 up. What is the function ?

• A
• B
• C
• D
• E

Q2:

The following graph is a transformation of the graph of . What is the function it represents? Write your answer in a form related to the transformation. • A
• B
• C
• D
• E

Q3:

This is the graph of . Which of the following is the graph of ?  • A(c)
• B(b)
• C(a)

Q4:

Consider the following graph of the linear function . Which of the following is the graph of the function ? • A(d)
• B(a)
• C(b)
• D(c)

Q5:

Which of the following is the graph of ?  • A(c)
• B(d)
• C(a)
• D(b)

Q6:

Which function is represented below? • A
• B
• C
• D
• E

Q7:

The function is translated 2 units in the direction of the positive x-axis. What is the equation of the resulting function?

• A
• B
• C

Q8:

This is the graph of the exponential function . Which of the following is the graph of ?  • A(a)
• B(b)
• C(c)

Q9:

Which of the following processes would you use to obtain the graph of from the graph of ?

1. reflect the graph in the -axis
2. reflect the graph in the -axis
3. reflect the graph in the line
4. reflect the graph in the line
• Aa only
• Bd only
• Cb only
• Dc and d
• Ea and b

Q10:

The function is stretched in the horizontal direction by a scale factor of and in the vertical direction by a scale factor of . Write, in terms of , the equation of the transformed function.

• A
• B
• C
• D
• E

Q11:

The function is translated eight down. Write, in terms of , the equation of the translated graph.

• A
• B
• C
• D
• E

Q12:

The function is stretched in the horizontal direction by a scale factor of 2 and in the vertical direction by a scale factor of 2. Write, in terms of , the equation of the transformed function.

• A
• B
• C
• D
• E

Q13:

The function is stretched in the horizontal direction by a scale factor of . Write, in terms of , the equation of the transformed function.

• A
• B
• C
• D
• E

Q14:

Daniel thinks that he can map the graph of the function to the graph of any other linear function by a translation followed by a stretch. This is equivalent to saying that any linear function can be written in the form for suitable values of and .

Is he right?

• Ano
• Byes

Suppose that and is as before. Find and in terms of and when it is possible to write in the form .

• A,
• B,
• C,
• D,
• E,

Let and . Find the values of and for which . Use the following graph to help you. • A,
• B,
• C,
• D,
• E,

Q15:

Graphs and in the diagram are the graphs of square root functions. They are symmetric about the origin. The equation of graph is . Knowing that a point reflection about the origin is equivalent to a reflection in the -axis followed by a reflection in the -axis, find the equation of graph . • A
• B
• C
• D
• E

Q16:

Consider the function given by .

Which of the graphs in the given diagram is the reflection of the graph of in the ? • AH
• BE
• CF
• DG

Write its equation.

• A
• B
• C
• D

Q17:

Consider the function given by .

Which of the graphs in the given diagram is the reflection of the graph of in the -axis? • AG
• BC
• CE
• DA

Write its equation.

• A
• B
• C
• D

Q18:

Consider the function .

Which of the following is the graph of ? • AC
• BB
• CA
• DD

State the domain and range of .

• Bdomain: , range:
• Cdomain: , range:
• Ddomain: , range:

Q19:

Consider the function .

Which of the graphs shown in the given diagram is the reflection of in the -axis? • AE
• BF
• CH
• DG

Write its equation.

• A
• B
• C
• D

Q20:

Consider the function .

Which of the following is the graph of ? • BC
• CB
• DA

How would you describe the transformation from to ?

• Atranslation three units up
• Bdilation in the horizontal direction by a factor of 3
• Cdilation in the vertical direction by a factor of 3

State the domain and range of .

• Bdomain: , range:
• Cdomain: , range:

Q21:

Consider the function given by .

The function is obtained by dilating in the horizontal direction by a factor and translating it units horizontally. Write the equation for .

• A
• B
• C
• D

Find so that .

• A
• B
• C
• D

Find so that .

• A
• B
• C
• D

Use your previous answers to find the equation of the graph shown in the given diagram. • A
• B
• C
• D

Q22:

Consider the root function .

The function has been obtained by translating three units down and five units to the left. Write its equation.

• A
• B
• C
• D
• E

State the domain and range of .

• Bdomain: , range:
• Cdomain: , range:
• Ddomain: , range:
• Edomain: , range:

Q23:

Consider the function given by .

The function is obtained by dilating in the vertical direction by a factor and translating it units horizontally and units vertically. Write an equation for .

• A
• B
• C
• D

Where is the origin mapped to when transforming from the graph of to the graph of ?

• A
• B
• C
• D

Find .

• A
• B
• C
• D

Use your previous answers to find the equation of the graph shown in the given diagram. • A
• B
• C
• D

Q24:

Consider the function given by . Which of the shown graphs is the graph of ?

• AB
• BF
• CH
• DD

Which of the shown graphs is the reflection of the graph of in the -axis?

• AH
• BB
• CD
• DF

Write its equation.

• A
• B
• C
• D

Q25:

This is the graph of . Which of the following is the graph of ?  • A(c)
• B(a)
• C(b)