Question

Write a function that meets the given conditions.

Rational function; asymptotes:$y=2,x=4$, domain$\left\{x|x\ne 4,9\right\}$

Short answer

The possible rational function is$r\left(x\right)=\frac{2x^2}{(x-4)(x-9)}$

Step-by-step solution

Step 1. Given Information

The given data is asymptotes $y=2,x=4$: , domain$\left\{x|x\ne 4,9\right\}$

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 is$r\left(x\right)=\frac{2x^2}{(x-4)(x-9)}$