AP®︎ Precalculus: Topic 1.12 Practice Test

Prepare for your quiz, test, or the AP exam with focused practice questions on Topic 1.12 of AP Precalculus – Transformations of Functions.

Questions List

Topic 1.12

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Question 1 Easy

Which transformation of the graph of ff produces the graph of g(x)=f(x−4)g(x)=f(x-4)?

AA translation 4 units up.
BA translation 4 units left.
CA translation 4 units right.
DA translation 4 units down.

What You’re Being Tested On:

Explore the learning objectives taken directly from the College Board’s AP® Precalculus Curriculum. Ensure you’re prepared for the exact topics covered on the AP® exam, in-class tests, and quizzes, and gain confidence in your mastery of the material.

Topic 1.12: Transformations of Functions

Learning Objective: 1.12.A

Construct a function that is an additive and/or multiplicative transformation of another function.

Essential Knowledge: 1.12.A.1

The function g(x)=f(x)+kg(x) = f(x) + k is an additive transformation of the function ff that results in a vertical translation of the graph of ff by kk units.

Essential Knowledge: 1.12.A.2

The function g(x)=f(x+h)g(x) = f(x + h) is an additive transformation of the function ff that results in a horizontal translation of the graph of ff by −h-h units.

Essential Knowledge: 1.12.A.3

The function g(x)=af(x)g(x) = af(x), where a≠0a \ne 0, is a multiplicative transformation of the function ff that results in a vertical dilation of the graph of ff by a factor of ∣a∣|a|. If a<0a < 0, the transformation involves a reflection over the xx-axis.

Essential Knowledge: 1.12.A.4

The function g(x)=f(bx)g(x) = f(bx), where b≠0b \ne 0, is a multiplicative transformation of the function ff that results in a horizontal dilation of the graph of ff by a factor of ∣1b∣\left|\frac{1}{b}\right|. If b<0b < 0, the transformation involves a reflection over the yy-axis.

Essential Knowledge: 1.12.A.5

Additive and multiplicative transformations can be combined, resulting in combinations of horizontal and vertical translations and dilations. The set of points prior to the transformations is called the preimage of the transformations, and the set of points after the transformations is called the image of the transformations.

Essential Knowledge: 1.12.A.6

The domain and range of a function that is a transformation of a parent function may be different from those of the parent function.

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