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Chapter 4: Q. 9 (page 247)

Write a function that meets the given conditions.

Rational function; asymptotes:y=2,x=4, domainx|x鈮�4,9

Short Answer

Expert verified

The possible rational function isr(x)=2x2(x-4)(x-9)

Step by step solution

01

Step 1. Given Information

The given data is asymptotes y=2,x=4: , domainx|x鈮�4,9

02

Step 2. Explanation

From the given domain of the function, the denominator is 0 when x=4andx=9

Thus, the factor of denominator can be written as (x-4)(x-9)

Since y=2, the ratio of the coefficients of the numerator and denominator is 2. since, the degree of the denominator is 2, the numerator must also have a degree of 2.

Thus, one possible choice of rational function isr(x)=2x2(x-4)(x-9)

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