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

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

 

Expert Solution
Step 1

The notation limxa+ implies the limit calculated by approaching the point x=a from the right. The notation limxa- implies the limit calculated by approaching the point x=a from the left. 

If for a function limx±f(x)=a the it has the horizontal asymptote y=a. If the function tends to ± as xa 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 limxf(x). From the graph we see that as x the function approaches the line y=5.

Hence, limxf(x)=5.

 

15.

Limit to be calculated is limx-f(x). From the graph we see that as x- the function approaches the line y=5.

Hence, limx-f(x)=5.

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