# Worksheet: Function Transformations: Translations

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

**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)

**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 ?

- reflect the graph in the -axis
- reflect the graph in the -axis
- reflect the graph in the line
- 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 .

- Adomain: , range:
- 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 ?

- AD
- 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 .

- Adomain: , range:
- 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 .

- Adomain: , range:
- 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)