Algebra 2 Practice Test: Transformations of Functions
- Transformations of Functions
- 10 questions
- 13 minutes
These 10 questions cover how changes to a function rule move or reshape its graph. Tip: changes inside the parentheses act on x and often work the opposite way you expect.
Tap an option to mark your answer. You can change your mind, or tap the same option again to leave the question blank. The correct answers and explanations appear when you finish the test.Tap an option to answer; tap it again to leave the question blank.
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Question 1
How is the graph of g(x) = (x − 3)2 + 2 related to the graph of f(x) = x2?
Correct answer: C
Subtracting 3 inside moves the graph right 3, and adding 2 outside moves it up 2. Reading (x − 3) as a left shift is the most common sign mistake.
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Question 2
Which transformation maps y = |x| onto y = −|x|?
Correct answer: A
Multiplying the output by −1 flips every point (x, y) to (x, −y), a reflection over the x-axis. Reflecting |x| over the y-axis would not change it at all.
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Question 3
How is the graph of y = x + 5 related to the graph of y = x?
Correct answer: D
Adding 5 inside the function moves the graph 5 units left; the starting point moves from (0, 0) to (−5, 0).
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Question 4
The graph of g(x) = f(−x) is the graph of f after which transformation?
Correct answer: B
Replacing x with −x changes each point (a, b) to (−a, b), which mirrors the graph across the y-axis.
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Question 5
The graph of y = |x| is stretched vertically by a factor of 3 and then shifted 4 units down. Which equation describes the new graph?
Correct answer: C
The stretch multiplies the outputs: 3|x|. Shifting down afterwards subtracts 4: 3|x| − 4. The answer 3|x| − 12 would be a shift down of 12.
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Question 6
The point (2, 5) is on the graph of y = f(x). Which point must be on the graph of y = f(x − 4) + 1?
Correct answer: B
The graph moves 4 units right and 1 unit up, so (2, 5) goes to (2 + 4, 5 + 1) = (6, 6).
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Question 7
The point (6, −1) is on the graph of y = f(x). Which point must be on the graph of y = f(2x)?
Correct answer: A
f(2x) compresses the graph horizontally by a factor of 12. Since 2(3) = 6, the new graph has y = f(6) = −1 at x = 3.
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Question 8
The graph of y = x3 has its point of symmetry at (0, 0). Where is the point of symmetry of y = (x + 1)3 − 7?
Correct answer: C
The graph moves 1 unit left and 7 units down, so the center moves from (0, 0) to (−1, −7).
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Question 9
What is the horizontal asymptote of y = 2x − 3?
Correct answer: A
y = 2x approaches 0 for very negative x. Shifting the graph down 3 moves that asymptote to y = −3.
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Question 10
If f(x) = x2, what is the range of g(x) = −2f(x) + 5?
Correct answer: D
x2 ≥ 0, so −2x2 ≤ 0 and −2x2 + 5 ≤ 5. The reflection turns the parabola upside down, so the vertex (0, 5) is a maximum.
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