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Chapter 1: Q. 22 (page 149)

Find the equation of a rational function that could have the graph shown. Take into account roots, holes, and vertical and horizontal asymptotes when constructing your function.

Short Answer

Expert verified

Ans:(x)=x1鈭�x2:鈭�1<x<12x1鈭�x2+2:x>12x1鈭�x2+2:x<鈭�1

Step by step solution

01

Step 1. Given information.

given,

the rational function that could have the graph given in the question.

02

Step 2. The function would be 

(x)=x1鈭�x2:鈭�1<x<12x1鈭�x2+2:x>12x1鈭�x2+2:x<鈭�1

03

Step 3. Now the graph of the function is given below 

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Most popular questions from this chapter

Write delta-epsilon proofs for each of the limit statements limx鈫�cfx=Lin Exercises 47-60.

limx鈫�23-4x=-5.

For each limit in Exercises 33鈥�38, either use continuity to calculate the limit or explain why Theorem 1.16 does not apply.

limx鈫�-5(3x-2).

Sketch the graph of a function f described in Exercises 27鈥�32, if possible. If it is not possible, explain why not.

f is left continuous at x = 1 and right continuous at x = 1, but is not continuous at x = 1, and f(1) = 鈭�2.

Sketch a labeled graph of a function that fails to satisfy the hypothesis of the Intermediate Value Theorem, and illustrate on your graph that the conclusion of the Intermediate Value Theorem does not necessarily hold.

For each limit in Exercises 33鈥�38, either use continuity to calculate the limit or explain why Theorem 1.16 does not apply.

limx鈫�-16.
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