Consider the function below. x2 x² - 4 f(x)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 54E
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Consider the function below.
f(x)
- 4
Exercise (a)
Find the vertical and horizontal asymptotes.
Step 1
To find horizontal asymptotes, we need to let x → ±o.
.2
we should divide the numerator and denominator by x
4
To find
lim
We
have:
x²/x²
lim
lim
lim
x t0 (x2 - 4)/x²
- 4
1 - 4/x2
%3D
1 - 0
So the horizontal asymptote is the line y =
1
Step 2
There will be vertical asymptotes at points where the denominator is 0. This happens when x = 2 and x =
-2
-2
Step 3
As x→ -2-,
and
- 4 →
So the
lim
x → -2- x2
4
Therefore, the line x =
is a vertical asymptote.
Transcribed Image Text:Consider the function below. f(x) - 4 Exercise (a) Find the vertical and horizontal asymptotes. Step 1 To find horizontal asymptotes, we need to let x → ±o. .2 we should divide the numerator and denominator by x 4 To find lim We have: x²/x² lim lim lim x t0 (x2 - 4)/x² - 4 1 - 4/x2 %3D 1 - 0 So the horizontal asymptote is the line y = 1 Step 2 There will be vertical asymptotes at points where the denominator is 0. This happens when x = 2 and x = -2 -2 Step 3 As x→ -2-, and - 4 → So the lim x → -2- x2 4 Therefore, the line x = is a vertical asymptote.
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