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