AP PreCalculus Flashcards: Transformations of Functions
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 16 cards to help you master important concepts.
What is the effect of the transformation g(x) = f(bx), where b ≠ 0?
This transformation causes a horizontal dilation of the graph of f(x) by a factor of |1/b|. If |b| > 1, it's a compression; if 0 < |b| < 1, it's a stretch.
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What is the effect of the transformation g(x) = f(bx), where b ≠ 0?
This transformation causes a horizontal dilation of the graph of f(x) by a factor of |1/b|. If |b| > 1, it's a compression; if 0 < |b| < 1, it's a stretch.
Construct a function g(x) that horizontally compresses f(x) by a factor of 1/2 and then shifts it down by 1 unit.
The function would be constructed as g(x) = f(2x) - 1.
Can different types of transformations be applied to a single function?
Yes, additive and multiplicative transformations can be combined, resulting in a sequence of translations and dilations.
Construct a function g(x) that shifts f(x) to the right by 2 units and then vertically stretches it by a factor of 3.
The function would be constructed as g(x) = 3 * f(x - 2).
Describe the transformation from f(x) to g(x) = f(x/4).
This is equivalent to g(x) = f((1/4)x), which is a horizontal stretch of the graph of f(x) by a factor of 4.
How would you write a function g(x) that shifts the graph of f(x) down by 7 units?
The new function would be g(x) = f(x) - 7.
Can transformations of a function change its domain and range?
Yes, the domain and range of a transformed function may be different from those of the parent function, particularly with vertical shifts and dilations affecting the range.
What is a multiplicative transformation of a function?
A multiplicative transformation constructs a new function by multiplying the original function or its input by a constant, resulting in a vertical or horizontal dilation (stretch or compression).
What is the effect of the transformation g(x) = f(x) + k?
This transformation causes a vertical translation of the graph of f(x) by k units. If k is positive, the graph shifts up; if k is negative, it shifts down.
How does the graph of g(x) = f(x - 5) relate to the graph of f(x)?
The graph of g(x) is a horizontal translation of the graph of f(x) by 5 units to the right.
What is the effect of the transformation g(x) = a * f(x), where a ≠ 0?
This transformation causes a vertical dilation of the graph of f(x) by a factor of |a|. If |a| > 1, it's a stretch; if 0 < |a| < 1, it's a compression.
Describe the transformation from f(x) to g(x) = f(3x).
The graph of g(x) is a horizontal compression of the graph of f(x) by a factor of 1/3.
Define "horizontal dilation".
A horizontal dilation is a multiplicative transformation of the form g(x) = f(bx) that stretches or compresses the graph of a function horizontally.
Describe the transformation from f(x) to g(x) = (1/2)f(x).
The graph of g(x) is a vertical compression of the graph of f(x) by a factor of 1/2.
What is an additive transformation of a function?
An additive transformation constructs a new function by adding a constant to the original function or its input, resulting in a vertical or horizontal translation (shift).
What is the effect of the transformation g(x) = f(x + h)?
This transformation causes a horizontal translation of the graph of f(x) by -h units. For example, f(x+2) shifts the graph 2 units to the left.