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Chapter 4: Q. 45 (page 234)

In Problems 45-48, find a rational function that might have the given graph. (More than one answer might be possible.)

Short Answer

Expert verified

The function isR(x)=x2x2-4

Step by step solution

01

Given information

Given the graph

02

Checking the asymptote

Here there are two asymptotes namely

x=-2x=2so the denominator is of the formR(x)=A(x)(x+2)(x-2)

03

Checking the curve

The curve touches the xaxis at the origin so it have even multiplicity of two. Then the horizontal asymptote is one so the values of leading coefficient should be same i.e. one .So the function is

R(x)=x2x2-4

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Most popular questions from this chapter

One solution of the equation x3-8x2+16x-3=0 is 3.

Find the sum of the remaining solutions.

Solve the given inequality algebraically.

x3>1

In Problems 39鈥�56, find the real zeros of f. Use the real zeros to factor f.

f(x)=4x5+12x4-x-3

In Problems 63鈥�72, find the real solutions of each equation.

2x3+3x2+2x+3=0

In Problems 63鈥�72, find the real solutions of each equation.

2x3-3x2-3x-5=0
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