# Lesson Worksheet: Function Transformations: Translations Mathematics

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

**Q4: **

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:

**Q5: **

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:

**Q6: **

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

**Q8: **

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

**Q10: **

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

**Q11: **

The function is translated four up. Write, in terms of , the equation of the translated graph.

- A
- B
- C
- D
- E

**Q12: **

Graph (a) shows the curve , which has a point of inflection at the origin. Determine the equation of graph (b), given that it is a translation of graph (a).

- A
- B
- C
- D
- E

**Q13: **

The function is translated three to the right. Write, in terms of , the equation of the translated graph.

- A
- B
- C
- D
- E

**Q14: **

Let . For any function , what transformation takes the graph of to the graph of ?

- Aa translation right by 4 units
- Ba translation up by 4 units
- Ca translation down by 4 units
- Da translation left by 4 units
- Ea reflection in the line

**Q15: **

The following is the graph of the function , which takes a real number and returns its fractional part.

What are the values of , and ?

- A0, 0.35, 0.67
- B0, 4, 12,345
- C4, 4, 12,345
- D4, 0.35, 0.67
- E0, 0.35, 0.67

What are the values of and ? Be careful, this is not as straightforward as for positive inputs!

- A, 4
- B, 0.65
- C,
- D0.99,
- E0.99, 0.65

The following is the graph of the function .

By considering suitable translations, express in terms of .

- A
- B
- C
- D
- E

The following is the graph of the triangle function .

Use the absolute value function to express in terms of .

- A
- B
- C
- D
- E

**Q16: **

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

- A
- B
- C
- D
- E

**Q17: **

The figure shows the graph of .

Which of the following is the graph of ?

- A
- B
- C
- D
- E

**Q18: **

Which of the following equations could be that of the given graph?

- A
- B
- C
- D
- E

**Q19: **

Which of the graphs matches the equation ?

- AC
- BD
- CA
- DB

**Q20: **

The curve of the function is the same curve of the function by translation of magnitude 5Β units in which direction?

- A
- B
- C
- D

**Q21: **

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

- A
- B
- C
- D
- E

**Q22: **

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

- A
- B
- C
- D
- E

**Q23: **

The figure shows the graph of .

Which of the following is the graph of ?

- A
- B
- C
- D
- E

**Q24: **

The figure shows the graph of .

Which of the following is the graph of ?

- A
- B
- C
- D
- E

**Q25: **

The function is translated five to the left. Write, in terms of , the equation of the translated graph.

- A
- B
- C
- D
- E