Relate a function's graph to its inverse
12th grade (Year 13 in England) · 16 questions · Common Core: HSF.BF.B.4.C · England: A-level Pure Mathematics
Name
Date
Score/ 16
Question 1
The graph of y = f(x) passes through (0, −4). Which transformation maps it onto the graph of y = f⁻¹(x)?
- A. Reflection in the line y = −x
- B. Rotation of 180° about the origin
- C. Reflection in the line y = x
- D. Reflection in the y-axis
Question 2
f(x) = x³ + 1. Find f⁻¹(9).
Answer
Question 3
The point (−1, 8) is on the graph of y = f(x). Which point must be on the graph of y = f⁻¹(x)? Type it like (2, −1).
Answer
Question 4
The graph of y = f(x) passes through (6, −1). Which transformation maps it onto the graph of y = f⁻¹(x)?
- A. Reflection in the x-axis
- B. Rotation of 180° about the origin
- C. Reflection in the y-axis
- D. Reflection in the line y = x
Question 5
f(x) = x³ − 4. Find f⁻¹(−12).
Answer
Question 6
The point (−4, −2) is on the graph of y = f(x). Which point must be on the graph of y = f⁻¹(x)? Type it like (2, −1).
Answer
Question 7
The graph of y = f(x) passes through (−1, 4). Which transformation maps it onto the graph of y = f⁻¹(x)?
- A. Reflection in the line y = x
- B. Reflection in the x-axis
- C. Reflection in the y-axis
- D. Reflection in the line y = −x
Question 8
f(x) = x³ + 3. Find f⁻¹(11).
Answer
Question 9
The point (−8, −2) is on the graph of y = f(x). Which point must be on the graph of y = f⁻¹(x)? Type it like (2, −1).
Answer
Question 10
The graph of y = f(x) passes through (−6, 2). Which transformation maps it onto the graph of y = f⁻¹(x)?
- A. Rotation of 180° about the origin
- B. Reflection in the x-axis
- C. Reflection in the line y = −x
- D. Reflection in the line y = x
Question 11
f(x) = x³ + 6. Find f⁻¹(33).
Answer
Question 12
The point (−4, 1) is on the graph of y = f(x). Which point must be on the graph of y = f⁻¹(x)? Type it like (2, −1).
Answer
Question 13
The graph of y = f(x) passes through (−6, 5). Which transformation maps it onto the graph of y = f⁻¹(x)?
- A. Rotation of 180° about the origin
- B. Reflection in the line y = x
- C. Reflection in the x-axis
- D. Reflection in the line y = −x
Question 14
f(x) = x³ + 3. Find f⁻¹(30).
Answer
Question 15
The point (6, −5) is on the graph of y = f(x). Which point must be on the graph of y = f⁻¹(x)? Type it like (2, −1).
Answer
Question 16
The graph of y = f(x) passes through (−2, −2). Which transformation maps it onto the graph of y = f⁻¹(x)?
- A. Rotation of 180° about the origin
- B. Reflection in the y-axis
- C. Reflection in the x-axis
- D. Reflection in the line y = x
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