Find the x and y Intercepts f(x)=-1/3x^6

$f (x) = - \frac{1}{3} x^{6}$

Find the x-intercepts.

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

$0 = - \frac{1}{3} x^{6}$

Solve the equation.

Rewrite the equation as $- \frac{1}{3} x^{6} = 0$ .

$- \frac{1}{3} x^{6} = 0$

Multiply both sides of the equation by $- 3$ .

$- 3 (- \frac{1}{3} x^{6}) = - 3 \cdot 0$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 3 (- \frac{1}{3} x^{6})$ .

Combine $x^{6}$ and $\frac{1}{3}$ .

$- 3 (- \frac{x^{6}}{3}) = - 3 \cdot 0$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{x^{6}}{3}$ into the numerator.

$- 3 \frac{- x^{6}}{3} = - 3 \cdot 0$

Factor $3$ out of $- 3$ .

$3 (- 1) \frac{- x^{6}}{3} = - 3 \cdot 0$

Cancel the common factor.

$3 \cdot - 1 \frac{- x^{6}}{3} = - 3 \cdot 0$

Rewrite the expression.

$- - x^{6} = - 3 \cdot 0$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x^{6} = - 3 \cdot 0$

Multiply $x^{6}$ by $1$ .

$x^{6} = - 3 \cdot 0$

Simplify the right side.

Multiply $- 3$ by $0$ .

$x^{6} = 0$

Take the 6th root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt[6]{0}$

Simplify $\pm \sqrt[6]{0}$ .

Rewrite $0$ as $0^{6}$ .

$x = \pm \sqrt[6]{0^{6}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 0$

Plus or minus $0$ is $0$ .

$x = 0$

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 $y$ .

$y = - \frac{1}{3} \cdot {(0)}^{6}$

Solve the equation.

Remove parentheses.

$y = - \frac{1}{3} \cdot 0^{6}$

Remove parentheses.

$y = - \frac{1}{3} \cdot {(0)}^{6}$

Simplify $- \frac{1}{3} \cdot {(0)}^{6}$ .

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

$y = - \frac{1}{3} \cdot 0$

Multiply $- \frac{1}{3} \cdot 0$ .

Multiply $0$ by $- 1$ .

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

Multiply $0$ by $\frac{1}{3}$ .

$y = 0$

y-intercept(s) in point form.

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

List the intersections.

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

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

Find the x and y Intercepts f(x)=-1/3x^6

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