AP®MathsCollege BoardPrecalculusExam QuestionsPolynomial & Rational FunctionsTransformations of Functions

Transformations of Functions (College Board AP® Precalculus): Exam Questions

42 mins30 questions

Select a download format for Transformations of Functions

Scroll for more

Select an answer set to view for
Transformations of Functions

1
Sme Calculator
1 mark

The function space f has domain open square brackets negative 3 comma 5 close square brackets. The function g is defined by g open parentheses x close parentheses equals f open parentheses x plus 4 close parentheses.

Determine the domain of g. Show the work that leads to your answer.

How did you do?

2
Sme Calculator
1 mark

Let space f open parentheses x close parentheses equals ln open parentheses x close parentheses. The function g is defined by g open parentheses x close parentheses equals 0.5 f open parentheses x minus 1 close parentheses plus 4.

Find the value of g open parentheses 3 close parentheses as a decimal approximation. Show the work that leads to your answer.

How did you do?

3
Sme Calculator
3 marks

The graph of the function space f has the following features:

  • a vertical asymptote at x equals negative 3

  • a horizontal asymptote at space y equals 2

  • a space y-intercept at open parentheses 0 comma 6 close parentheses

The function g is defined by g open parentheses x close parentheses equals f open parentheses x close parentheses minus 5.

(i) Find the equation of the vertical asymptote of the graph of g.

(ii) Find the equation of the horizontal asymptote of the graph of g.

(iii) Find the coordinates of the y-intercept of the graph of g.

How did you do?

4
Sme Calculator
1 mark

The function space f has range open square brackets negative 2 comma 7 close square brackets. The function g is defined by g open parentheses x close parentheses equals negative 3 f open parentheses x close parentheses plus 5.

Determine the range of g. Show the work that leads to your answer.

How did you do?

5
Sme Calculator
2 marks

The function space f has zeros at x equals negative 1, x equals 2, and x equals 6. The function g is defined by g open parentheses x close parentheses equals f open parentheses 0.5 open parentheses x minus 3 close parentheses close parentheses.

Determine the zeros of g. Show the work that leads to your answer.

How did you do?

6
Sme Calculator
2 marks

The function space f has a maximum value of 8, which occurs at x equals negative 1. The function g is defined by g open parentheses x close parentheses equals 2 f open parentheses x plus 2 close parentheses plus 5.

Determine the maximum value of g and the value of x at which it occurs. Show the work that leads to your answer.

How did you do?

7
Sme Calculator
2 marks

The function space f has domain open square brackets negative 2.3 comma space 5.6 close square brackets. The function g is defined by g open parentheses x close parentheses equals f open parentheses 0.7 x minus 1.5 close parentheses.

Determine the domain of g. Express the endpoints of the interval as decimal approximations. Show the work that leads to your answer.

How did you do?

8
Sme Calculator
3 marks

The function space f has zeros at x equals negative 2 and x equals 4, and space f open parentheses 0 close parentheses equals negative 3. The graph of space f in the x y-plane has a vertical asymptote at x equals 6.

The function g is given by g open parentheses x close parentheses equals f open parentheses negative 2 x close parentheses.

(i) Find all zeros of g.

(ii) Find the equation of the vertical asymptote of the graph of g.

(iii) Find g open parentheses 0 close parentheses.

How did you do?

9
Sme Calculator
2 marks

The function g is given by g open parentheses x close parentheses equals negative 1 half f open parentheses 3 x plus 12 close parentheses plus 5.

Describe the additive and multiplicative transformations that map the graph of space f to the graph of g.

How did you do?

10a
Sme Calculator
2 marks

The function space f has a maximum value of 5 at x equals 4. The function g is given by

g open parentheses x close parentheses equals a times f open parentheses b open parentheses x plus h close parentheses close parentheses plus k

where a, b, h, and k are positive constants. The function g has a maximum value of 11 at x equals 1. The graph of g passes through open parentheses negative 1 comma space 3 close parentheses, which is the image of the point open parentheses 0 comma space 1 close parentheses on the graph of space f under the transformation.

Find the values of b and h. Show the work that leads to your answer.

How did you do?

10b
Sme Calculator
2 marks

Find the values of a and k. Show the work that leads to your answer.

How did you do?

11
Sme Calculator
2 marks

The function space f has domain open square brackets negative 3.4 comma 8.2 close square brackets and range open square brackets negative 1.5 comma 4.3 close square brackets. The function g is defined by g open parentheses x close parentheses equals negative 2 f open parentheses 0.6 x plus 1.8 close parentheses plus 3.5.

(i) Find the domain of g. Express the endpoints of the interval as decimal approximations. Show the work that leads to your answer.

(ii) Find the range of g. Show the work that leads to your answer.

How did you do?