# How to write an equation for a rational function with: vertical asymptotes at x = 3 and x = -5?

Jun 8, 2018

$f \left(x\right) = \frac{1}{{x}^{2} + 2 x - 15}$

#### Explanation:

Function must be undefined at $x = 3$ and $x = - 5$, i.e. $f \left(x\right) = \frac{1}{0}$

Many functions will work but here is the simplest one:

$f \left(x\right) = \frac{1}{\left(x - 3\right) \left(x + 5\right)}$

$f \left(x\right) = \frac{1}{{x}^{2} + 2 x - 15}$

graph{1/(x^2+2x-15) [-10, 10, -5, 5]}