Sketch the graph of a function f(x) that satisfies all of the following properties. limx__) -infinity F(x)=-4 Limx__) infinity f(x)=3 x=-5 is a vertical asymptote for f f'(x)>on (−1,∞) f'(x)<0 on (−∞,−5) and (-5,-1) f'(-1)=0 f''(x)>0 on (-5,3) f''(x)<0 on (−∞,−5) and(3,∞) f''(3)=0

Sketch the graph of a function f(x) that satisfies all of the following properties. limx) -infinity F(x)=-4 Limx) infinity f(x)=3 x=-5 is a vertical asymptote for f f'(x)>on (−1,∞) f'(x)<0 on (−∞,−5) and (-5,-1) f'(-1)=0 f''(x)>0 on (-5,3) f''(x)<0 on (−∞,−5) and(3,∞) f''(3)=0

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.5: Rational Functions

Problem 8E

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Concept explainers

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.

Question

Sketch the graph of a function f(x) that satisfies all of the following properties.

lim_{x__) -infinity}F(x)=-4
Lim_{x__) infinity}f(x)=3
x=-5 is a vertical asymptote for f
f'(x)>on (−1,∞)
f'(x)<0 on (−∞,−5) and (-5,-1)
f'(-1)=0
f''(x)>0 on (-5,3)
f''(x)<0 on (−∞,−5) and(3,∞)
f''(3)=0

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