AP®︎ Precalculus: Topic 1.9 Practice Test

Prepare for your quiz, test, or the AP exam with focused practice questions on Topic 1.9 of AP Precalculus – Rational Functions and Vertical Asymptotes.

Questions List

Topic 1.9

Q1
Q2
Q3
Q4
Q5
Q6
Q7
Q8
Q9
Q10
Q11
Q12
Q13
Q14
Q15

Question 1 Easy

Let r(x)=x+4(x−1)(x+5)r(x)=\dfrac{x+4}{(x-1)(x+5)}.

Which of the following gives all vertical asymptotes of the graph of rr?

Ax=−4x=-4
Bx=1x=1 and x=−5x=-5
Cx=−1x=-1 and x=5x=5
Dx=1x=1, x=−5x=-5, and x=−4x=-4

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 1.9: Rational Functions and Vertical Asymptotes

Learning Objective: 1.9.A

Determine vertical asymptotes of graphs of rational functions.

Essential Knowledge: 1.9.A.1

If the value aa is a real zero of the polynomial function in the denominator of a rational function and is not also a real zero of the polynomial function in the numerator, then the graph of the rational function has a vertical asymptote at x=ax=a. Furthermore, a vertical asymptote also occurs at x=ax=a if the multiplicity of aa as a real zero in the denominator is greater than its multiplicity as a real zero in the numerator.

Essential Knowledge: 1.9.A.2

Near a vertical asymptote, x=ax=a, of a rational function, the values of the polynomial function in the denominator are arbitrarily close to zero, so the values of the rational function rr increase or decrease without bound. The corresponding mathematical notation is lim⁡x→a+r(x)=∞\lim_{x\to a^+}r(x)=\infty or lim⁡x→a+r(x)=−∞\lim_{x\to a^+}r(x)=-\infty for input values near aa and greater than aa, and lim⁡x→a−r(x)=∞\lim_{x\to a^-}r(x)=\infty or lim⁡x→a−r(x)=−∞\lim_{x\to a^-}r(x)=-\infty for input values near aa and less than aa.

Also applying to college?Free college essay reviewGet your college essay graded