Find the x and y Intercepts f(x)=1/(3x^2+3x-18)

$f (x) = \frac{1}{3 x^{2} + 3 x - 18}$

Step 1

Find the x-intercepts.

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

$0 = \frac{1}{3 x^{2} + 3 x - 18}$

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 2

Find the y-intercepts.

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

$y = \frac{1}{3 {(0)}^{2} + 3 (0) - 18}$

Solve the equation.

Remove parentheses.

$y = \frac{1}{3 \cdot 0^{2} + 3 (0) - 18}$

Remove parentheses.

$y = \frac{1}{3 {(0)}^{2} + 3 (0) - 18}$

Simplify $\frac{1}{3 {(0)}^{2} + 3 (0) - 18}$ .

Simplify the denominator.

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

$y = \frac{1}{3 \cdot 0 + 3 (0) - 18}$

Multiply $3$ by $0$ .

$y = \frac{1}{0 + 3 (0) - 18}$

Multiply $3$ by $0$ .

$y = \frac{1}{0 + 0 - 18}$

Add $0$ and $0$ .

$y = \frac{1}{0 - 18}$

Subtract $18$ from $0$ .

$y = \frac{1}{- 18}$

Move the negative in front of the fraction.

$y = - \frac{1}{18}$

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{1}{18})$

Step 3

List the intersections.

x-intercept(s): $None$

y-intercept(s): $(0, - \frac{1}{18})$

Step 4