Algebra Examples

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

Step 1

Find the x-intercepts.

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Step 1.1

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

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

Step 1.2

Solve the equation.

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Step 1.2.1

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

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

Step 1.2.2

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

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

Step 1.2.3

Simplify both sides of the equation.

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Step 1.2.3.1

Simplify the left side.

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Step 1.2.3.1.1

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

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Step 1.2.3.1.1.1

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

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

Step 1.2.3.1.1.2

Cancel the common factor of $3$ .

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Step 1.2.3.1.1.2.1

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

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

Step 1.2.3.1.1.2.2

Factor $3$ out of $- 3$ .

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

Step 1.2.3.1.1.2.3

Cancel the common factor.

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

Step 1.2.3.1.1.2.4

Rewrite the expression.

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

Step 1.2.3.1.1.3

Multiply.

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Step 1.2.3.1.1.3.1

Multiply $- 1$ by $- 1$ .

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

Step 1.2.3.1.1.3.2

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

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

Step 1.2.3.2

Simplify the right side.

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Step 1.2.3.2.1

Multiply $- 3$ by $0$ .

$x^{6} = 0$

Step 1.2.4

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

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

Step 1.2.5

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

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Step 1.2.5.1

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

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

Step 1.2.5.2

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

$x = \pm 0$

Step 1.2.5.3

Plus or minus $0$ is $0$ .

$x = 0$

Step 1.3

x-intercept(s) in point form.

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

Step 2

Find the y-intercepts.

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Step 2.1

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

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

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

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

Step 2.2.2

Remove parentheses.

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

Step 2.2.3

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

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Step 2.2.3.1

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

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

Step 2.2.3.2

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

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Step 2.2.3.2.1

Multiply $0$ by $- 1$ .

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

Step 2.2.3.2.2

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

$y = 0$

Step 2.3

y-intercept(s) in point form.

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

Step 3

List the intersections.

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

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

Step 4