# How do you find the x and y intercepts for R(x) = (3x) / (x^2 - 9)?

Mar 15, 2017

$\text{both intercepts } = 0$

#### Explanation:

To find the intercepts.

• " substitute x = 0, in R(x), for y- intercept"

• " substitute y = 0, in R(x), for x-intercept"

$x = 0 \to R \left(0\right) = \frac{0}{0 - 9} = \frac{0}{- 9} = 0 \leftarrow \textcolor{red}{\text{ y-intercept}}$

The denominator of R(x) cannot be zero as this would make R(x) undefined. The numerator can, however, equal zero.

$y = 0 \to 3 x = 0 \to x = 0 \leftarrow \textcolor{red}{\text{ x-intercept}}$

That is R(x) passes through the origin (0 ,0)
graph{(3x)/(x^2-9) [-10, 10, -5, 5]}