AP Precalculus Transformations of Functions Drill 1

About This Drill

AP Precalculus Transformations of Functions Drill 1 is a Math practice drill covering Transformations of Functions. It contains 5 original questions created by Brian Stewart, a Barron's test prep author with over 20 years of tutoring experience.

Practice AP® Precalculus transformations of functions, including horizontal and vertical shifts, dilations, and combined transformations. These questions reflect the style and rigor of Topic 1.12 on the official exam.

Questions in This Drill

1. The graph of a function f is shown below.
   
   
   
   Which of the following describes the graph of g(x) = f(x + 1) − 2 compared to the graph of f?
2. Let f(x) = x² − 4x + 1. Which of the following defines g(x) = f(x − 3)?
3. The graph of a function f is shown below.
   
   
   
   The function g is defined by g(x) = 2f(x). Which of the following best describes the relationship between the graphs of f and g?
4. The function h is defined by h(x) = f(3x − 6), where f is a function. Which of the following correctly identifies the horizontal dilation factor and horizontal translation applied to f to produce h?
5. The graph of a function f is shown below.
   
   
   
   The function g is defined by g(x) = f(2(x − 4)). A student claims: “The graph of g is obtained by translating the graph of f right 4 units and then compressing it horizontally by a factor of ½.” Is the student’s claim correct?