AP®︎ Precalculus: Topic 1.10 Practice Test

Prepare for your quiz, test, or the AP exam with focused practice questions on Topic 1.10 of AP Precalculus – Rational Functions and Holes.

Questions List

Topic 1.10

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Q2
Q3
Q4
Q5
Q6
Q7
Q8
Q9
Q10
Q11
Q12

Question 1 Easy

Let r(x)=(x−4)(x+1)(x−4)(x−2)r(x)=\dfrac{(x-4)(x+1)}{(x-4)(x-2)}.

The graph of rr has a hole at which value of xx?

Ax=4x=4
Bx=−4x=-4
Cx=−1x=-1
Dx=2x=2

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 1.10: Rational Functions and Holes

Learning Objective: 1.10.A

Determine holes in graphs of rational functions.

Essential Knowledge: 1.10.A.1

If the multiplicity of a real zero in the numerator is greater than or equal to its multiplicity in the denominator, then the graph of the rational function has a hole at the corresponding input value.

Essential Knowledge: 1.10.A.2

If the graph of a rational function rr has a hole at x=cx=c, then the location of the hole can be determined by examining the output values corresponding to input values sufficiently close to cc. If input values sufficiently close to cc correspond to output values arbitrarily close to LL, then the hole is located at the point with coordinates (c,L)(c,L). The corresponding mathematical notation is lim⁡x→cr(x)=L\lim_{x\to c}r(x)=L. It should be noted that lim⁡x→c−r(x)=lim⁡x→c+r(x)=lim⁡x→cr(x)=L\lim_{x\to c^-}r(x)=\lim_{x\to c^+}r(x)=\lim_{x\to c}r(x)=L.

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