Chapter 1: Q. 31 (page 120)

Sketch the graph of a function f described in Exercises 27–32, if possible. If it is not possible, explain why not.
$f h a s a r e m o v a b l e d i s c o n t i n u i t y a t x = - 2 a n d i s r i g h t c o n t i n u o u s a t x = - 2, a n d f (- 2) = 0 .$

Short Answer

Expert verified

Function not possible.

Step by step solution

Step 1. Given Information.

Given:

$f (- 2) = 0, f i s r i g h t c o n t i n u o u s a t x = - 2, a n d i t h a s a r e m o v a b l e d i s c o n t i n u i t y a t x = - 2 .$

Step 2. Why function is not possible.

Now see that we are given that f has a removable discontinuity at $x = - 2$ this means the graph has a hole or a point at $x = - 2$ but just below in the second condition it is given that the absolute value of the function at $x = - 2$ is 0 which is a contradiction to it's own given condition.

Therefore, the function doesn't exist with these given conditions and so as the graph.

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Sketch the graph of a function f described in Exercises 27–32, if possible. If it is not possible, explain why not.
$f h a s a r e m o v a b l e d i s c o n t i n u i t y a t x = - 2 a n d i s r i g h t c o n t i n u o u s a t x = - 2, a n d f (- 2) = 0 .$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Why function is not possible.

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Sketch the graph of a function f described in Exercises 27–32, if possible. If it is not possible, explain why not.fhasaremovablediscontinuityatx=−2andisrightcontinuousatx=−2,andf(−2)=0.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Why function is not possible.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

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Study anywhere. Anytime. Across all devices.

Sketch the graph of a function f described in Exercises 27–32, if possible. If it is not possible, explain why not.
$f h a s a r e m o v a b l e d i s c o n t i n u i t y a t x = - 2 a n d i s r i g h t c o n t i n u o u s a t x = - 2, a n d f (- 2) = 0 .$