Find the x and y Intercepts f(x)=(x-4)/(2x+5)

$f (x) = \frac{x - 4}{2 x + 5}$

Find the x-intercepts.

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

$0 = \frac{x - 4}{2 x + 5}$

Solve the equation.

Set the numerator equal to zero.

$x - 4 = 0$

Add $4$ to both sides of the equation.

$x = 4$

x-intercept(s) in point form.

x-intercept(s): $(4, 0)$

Find the y-intercepts.

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

$y = \frac{(0) - 4}{2 (0) + 5}$

Solve the equation.

Remove parentheses.

$y = \frac{0 - 4}{2 (0) + 5}$

Remove parentheses.

$y = \frac{(0) - 4}{2 (0) + 5}$

Simplify $\frac{(0) - 4}{2 (0) + 5}$ .

Subtract $4$ from $0$ .

$y = \frac{- 4}{2 (0) + 5}$

Simplify the denominator.

Multiply $2$ by $0$ .

$y = \frac{- 4}{0 + 5}$

Add $0$ and $5$ .

$y = \frac{- 4}{5}$

Move the negative in front of the fraction.

$y = - \frac{4}{5}$

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{4}{5})$

List the intersections.

x-intercept(s): $(4, 0)$

y-intercept(s): $(0, - \frac{4}{5})$