# 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)

**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)

**Q12: **

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

**Q13: **

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,

**Q14: **

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:

**Q15: **

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:

**Q16: **

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

**Q17: **

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:

**Q18: **

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

**Q19: **

This is the graph of .

Which of the following is the graph of ?

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

**Q20: **

The figure shows the graph of and the point . The point is a local maximum. Identify the corresponding local maximum for the transformation .

- A
- B
- C
- D
- E

**Q21: **

The figure shows the graph of and the point . The point is a local maximum. Identify the corresponding local maximum for the transformation .

- A
- B
- C
- D
- E

**Q22: **

The red graph in the figure has equation and the black graph has equation . Express as a transformation of .

- A
- B
- C
- D
- E

**Q23: **

The figure shows the graph of and point . Point is a local maximum. Identify the corresponding local maximum for the transformation .

- A
- B
- C
- D
- E

**Q24: **

The figure shows the graph of and point , which is a local maximum. Identify the corresponding local maximum for the transformation .

- A
- B
- C
- D
- E

**Q25: **

The figure shows the graph of and the point . The point is a local maximum. Identify the corresponding local maximum for the transformation .

- A
- B
- C
- D
- E