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Chapter 4: Q. 61 (page 236)

Create a rational function that has the following characteristics: crosses the x-axis at 3; touches the x-axis at -2; one vertical asymptote, x=1; and one horizontal asymptote, y=2. Give your rational function to a fellow classmate and ask for a written critique of your rational function.

Short Answer

Expert verified

The rational function is2(x+2)(x-1)2(x-1)3.

Step by step solution

01

Step 1. Finding numerator of the rational function.

Here we have to find the rational through the given information First of all x intercept of the function is:

It touches the x-axis at -2.

It crosses the x-axis at 3.

And also it has a horizontal asymptote as y=2

From here we can write the numerator which is 2(x+2)(x-1)2.

02

Step 2. Finding rational function.

Now for denominator we are given that the vertical asymptote is at x=1and also it has been given that the horizontal asymptote of the function is y=2.

For any function to have a horizontal asymptote, the degree of the numerator and the denominator must be equal.

From this we have the denominator (x-1)3.

So the rational function is2(x+2)(x-1)2(x-1)3.

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Most popular questions from this chapter

Analyze each polynomial function using Steps 1through 8:

f(x)=x4+x3-3x2-x+2.

Solve the inequality algebraically.

x3+2x2-3x>0

Solve the inequality algebraically

(x-1)(x-2)(x-3)鈮�0

Find the domain of the rational function.

G(x)=x-3x2+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
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