This document contains a math lab exercise on graphing rational functions with 4 questions. Question 1 has students predict holes in graphs of rational functions. Question 2 has students predict vertical asymptotes. Question 3 has students predict which graphs have horizontal asymptotes. The document provides step-by-step solutions and explanations for each question.

1. 02_ch02_pre-calculas12_wncp_solution.qxd 5/16/12 11:08 PM Page 8
Home Quit
Lesson 2.2 Math Lab: Assess Your Understanding, page 104
Use graphing technology to check your answers.
1. Without graphing, predict whether the graph of each function has a
hole. State the related non-permissible value.
x2 - 16 x2 + 5
a) y = b) y =
x + 4 x2 - 25
(x ؊ 4)(x ؉ 4) x2 ؉ 5
y‫؍‬ y‫؍‬
x؊4 (x ؊ 5)(x ؉ 5)
The graph has a hole at The graph does not have a hole.
x ‫.4؊ ؍‬
2. Without graphing, predict the equations of any vertical asymptotes
for the graph of each function.
2x + 1 x2 - 2
a) y = x b) y =
x2 - 16
x ‫ 0 ؍‬is a vertical x2 ؊ 2
y‫؍‬
asymptote. (x ؊ 4)(x ؉ 4)
x ‫ 4 — ؍‬are vertical asymptotes.
3x x - 2
c) y = 2 d) y = 2
x + 2 x + 7x + 10
The denominator is always x؊2
y‫؍‬
positive, so no vertical (x ؉ 2)(x ؉ 5)
asymptote. x ‫ 2؊ ؍‬and x ‫ 5؊ ؍‬are vertical
asymptotes.
3. Without graphing, predict which graphs of these functions have
horizontal asymptotes.
x + 3 2x2 + 6x
a) y = b) y =
2x2 + 6x x + 3
The degree of the numerator is The degree of the numerator is
less than the degree of the greater than the degree of the
denominator, so there is a denominator, so there is no
horizontal asymptote. horizontal asymptote.
8 2.2 Math Lab: Graphing Rational Functions—Solutions DO NOT COPY. ©P