Find the x and y Intercepts f(x)=x/(1+3x)

$f (x) = \frac{x}{1 + 3 x}$

Find the x-intercepts.

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

$0 = \frac{x}{1 + 3 x}$

Set the numerator equal to zero.

$x = 0$

x-intercept(s) in point form.

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

Find the y-intercepts.

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

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

Solve the equation.

Remove parentheses.

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

Simplify $\frac{0}{1 + 3 (0)}$ .

Simplify the denominator.

Multiply $3$ by $0$ .

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

Add $1$ and $0$ .

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

Divide $0$ by $1$ .

$y = 0$

y-intercept(s) in point form.

y-intercept(s): $(0, 0)$

List the intersections.

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

y-intercept(s): $(0, 0)$