Find the x and y Intercepts 1/(x^2-9)

$\frac{1}{x^{2} - 9}$

Step 1

Write $\frac{1}{x^{2} - 9}$ as an equation.

$y = \frac{1}{x^{2} - 9}$

Step 2

Find the x-intercepts.

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = \frac{1}{x^{2} - 9}$

Solve the equation.

Set the numerator equal to zero.

$1 = 0$

Since $1 \neq 0$ , there are no solutions.

No solution

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

x-intercept(s): $None$

Step 3

Find the y-intercepts.

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = \frac{1}{{(0)}^{2} - 9}$

Solve the equation.

Remove parentheses.

$y = \frac{1}{0^{2} - 9}$

Remove parentheses.

$y = \frac{1}{{(0)}^{2} - 9}$

Simplify $\frac{1}{{(0)}^{2} - 9}$ .

Simplify the denominator.

Raising $0$ to any positive power yields $0$ .

$y = \frac{1}{0 - 9}$

Subtract $9$ from $0$ .

$y = \frac{1}{- 9}$

Move the negative in front of the fraction.

$y = - \frac{1}{9}$

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{1}{9})$

Step 4

List the intersections.

x-intercept(s): $None$

y-intercept(s): $(0, - \frac{1}{9})$

Step 5