Answered: In Problems 14-17, refer to the…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Question

In Problems 14-17, refer to the following graph of y = f(x)

Expert Solution

Step 1

The notation $\lim_{x \to a^{+}}$ implies the limit calculated by approaching the point $x = a$ from the right. The notation $\lim_{x \to a^{-}}$ implies the limit calculated by approaching the point $x = a$ from the left.

If for a function $\lim_{x \to \pm \infty} f (x) = a$ the it has the horizontal asymptote $y = a$ . If the function tends to $\pm \infty$ as $x \to a$ then the function has a vertical asymptote $x = a$ .

Step 2

From the graph it is clear that function has horizontal asymptote $y = 5$ and has a vertical asymptote $x = 2$ .

14.

Limit to be calculated is $\lim_{x \to \infty} f (x)$ . From the graph we see that as $x \to \infty$ the function approaches the line $y = 5$ .

Hence, $\lim_{x \to \infty} f (x) = 5$ .

15.

Limit to be calculated is $\lim_{x \to - \infty} f (x)$ . From the graph we see that as $x \to - \infty$ the function approaches the line $y = 5$ .

Hence, $\lim_{x \to - \infty} f (x) = 5$ .

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