Question

How to find a rational function given 2 vertical asymptotes and an X intercept?

It’s question 20 by the way

Answer 1

`(x-4)/((x+3)(x-5))`

Explanation:

Since the rational function has vertical asymptotes at -3, and 5, the denominator must equal 0 when x is -3 or 5. Therefore, the denominator must be:

(x+3)(x-5)

Now, to make the x-intercept at (4, 0), the numerator must be equal to 0 when x is 4. Therefore, the numerator must be:

x-4

Therefore, that rational function is:

`(x-4)/((x+3)(x-5_)`