Find the x and y Intercepts y = cube root of x-2

$y = \sqrt[3]{x - 2}$

Step 1

Find the x-intercepts.

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

$0 = \sqrt[3]{x - 2}$

Solve the equation.

Rewrite the equation as $\sqrt[3]{x - 2} = 0$ .

$\sqrt[3]{x - 2} = 0$

To remove the radical on the left side of the equation, cube both sides of the equation.

${\sqrt[3]{x - 2}}^{3} = 0^{3}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{x - 2}$ as ${(x - 2)}^{\frac{1}{3}}$ .

${({(x - 2)}^{\frac{1}{3}})}^{3} = 0^{3}$

Simplify the left side.

Simplify ${({(x - 2)}^{\frac{1}{3}})}^{3}$ .

Multiply the exponents in ${({(x - 2)}^{\frac{1}{3}})}^{3}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(x - 2)}^{\frac{1}{3} \cdot 3} = 0^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(x - 2)}^{\frac{1}{3} \cdot 3} = 0^{3}$

Rewrite the expression.

${(x - 2)}^{1} = 0^{3}$

Simplify.

$x - 2 = 0^{3}$

Simplify the right side.

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

$x - 2 = 0$

Add $2$ to both sides of the equation.

$x = 2$

x-intercept(s) in point form.

x-intercept(s): $(2, 0)$

Step 2

Find the y-intercepts.

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

$y = \sqrt[3]{(0) - 2}$

Simplify $\sqrt[3]{(0) - 2}$ .

Subtract $2$ from $0$ .

$y = \sqrt[3]{- 2}$

Rewrite $- 2$ as ${(- 1)}^{3} \cdot 2$ .

Rewrite $- 2$ as $- 1 (2)$ .

$y = \sqrt[3]{- 1 (2)}$

Rewrite $- 1$ as ${(- 1)}^{3}$ .

$y = \sqrt[3]{{(- 1)}^{3} \cdot 2}$

Pull terms out from under the radical.

$y = - 1 \sqrt[3]{2}$

Rewrite $- 1 \sqrt[3]{2}$ as $- \sqrt[3]{2}$ .

$y = - \sqrt[3]{2}$

y-intercept(s) in point form.

y-intercept(s): $(0, - \sqrt[3]{2})$

Step 3

List the intersections.

x-intercept(s): $(2, 0)$

y-intercept(s): $(0, - \sqrt[3]{2})$

Step 4

Find the x and y Intercepts y = cube root of x-2

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