Find the x and y Intercepts f(x)=(2x-18)/(25x^2-81)

$f (x) = \frac{2 x - 18}{25 x^{2} - 81}$

Step 1

Find the x-intercepts.

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

$0 = \frac{2 x - 18}{25 x^{2} - 81}$

Solve the equation.

Set the numerator equal to zero.

$2 x - 18 = 0$

Solve the equation for $x$ .

Add $18$ to both sides of the equation.

$2 x = 18$

Divide each term in $2 x = 18$ by $2$ and simplify.

Divide each term in $2 x = 18$ by $2$ .

$\frac{2 x}{2} = \frac{18}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{18}{2}$

Divide $x$ by $1$ .

$x = \frac{18}{2}$

Simplify the right side.

Divide $18$ by $2$ .

$x = 9$

x-intercept(s) in point form.

x-intercept(s): $(9, 0)$

Step 2

Find the y-intercepts.

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

$y = \frac{2 (0) - 18}{25 {(0)}^{2} - 81}$

Solve the equation.

Remove parentheses.

$y = \frac{2 (0) - 18}{25 \cdot 0^{2} - 81}$

Remove parentheses.

$y = \frac{2 (0) - 18}{25 {(0)}^{2} - 81}$

Simplify $\frac{2 (0) - 18}{25 {(0)}^{2} - 81}$ .

Simplify the numerator.

Multiply $2$ by $0$ .

$y = \frac{0 - 18}{25 \cdot 0^{2} - 81}$

Subtract $18$ from $0$ .

$y = \frac{- 18}{25 \cdot 0^{2} - 81}$

Simplify the denominator.

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

$y = \frac{- 18}{25 \cdot 0 - 81}$

Multiply $25$ by $0$ .

$y = \frac{- 18}{0 - 81}$

Subtract $81$ from $0$ .

$y = \frac{- 18}{- 81}$

Cancel the common factor of $- 18$ and $- 81$ .

Factor $- 9$ out of $- 18$ .

$y = \frac{- 9 (2)}{- 81}$

Cancel the common factors.

Factor $- 9$ out of $- 81$ .

$y = \frac{- 9 \cdot 2}{- 9 \cdot 9}$

Cancel the common factor.

$y = \frac{- 9 \cdot 2}{- 9 \cdot 9}$

Rewrite the expression.

$y = \frac{2}{9}$

y-intercept(s) in point form.

y-intercept(s): $(0, \frac{2}{9})$

Step 3

List the intersections.

x-intercept(s): $(9, 0)$

y-intercept(s): $(0, \frac{2}{9})$

Step 4

Find the x and y Intercepts f(x)=(2x-18)/(25x^2-81)

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