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

$f (x) = 3 (3 x + 1)$

Step 1

Find the x-intercepts.

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

$0 = 3 (3 x + 1)$

Solve the equation.

Rewrite the equation as $3 (3 x + 1) = 0$ .

$3 (3 x + 1) = 0$

Divide each term in $3 (3 x + 1) = 0$ by $3$ and simplify.

Divide each term in $3 (3 x + 1) = 0$ by $3$ .

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $3 x + 1$ by $1$ .

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

Simplify the right side.

Divide $0$ by $3$ .

$3 x + 1 = 0$

Subtract $1$ from both sides of the equation.

$3 x = - 1$

Divide each term in $3 x = - 1$ by $3$ and simplify.

Divide each term in $3 x = - 1$ by $3$ .

$\frac{3 x}{3} = \frac{- 1}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 1}{3}$

Divide $x$ by $1$ .

$x = \frac{- 1}{3}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{1}{3}$

x-intercept(s) in point form.

x-intercept(s): $(- \frac{1}{3}, 0)$

Step 2

Find the y-intercepts.

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

$y = 3 (3 (0) + 1)$

Solve the equation.

Remove parentheses.

$y = 3 (3 (0) + 1)$

Simplify $3 (3 (0) + 1)$ .

Multiply $3$ by $0$ .

$y = 3 (0 + 1)$

Add $0$ and $1$ .

$y = 3 \cdot 1$

Multiply $3$ by $1$ .

$y = 3$

y-intercept(s) in point form.

y-intercept(s): $(0, 3)$

Step 3

List the intersections.

x-intercept(s): $(- \frac{1}{3}, 0)$

y-intercept(s): $(0, 3)$

Step 4

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

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