Find the Vertical and Horizontal Intercept(s) f(x) = cube root of x

$f (x) = \sqrt[3]{x}$

Step 1

Find the x-intercepts.

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

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

Solve the equation.

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

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

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

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

Simplify each side of the equation.

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

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

Simplify the left side.

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

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

$x^{1} = 0^{3}$

Simplify.

$x = 0^{3}$

Simplify the right side.

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

$x = 0$

x-intercept(s) in point form.

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

Step 2

Find the y-intercepts.

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

$y = \sqrt[3]{0}$

Simplify $\sqrt[3]{0}$ .

Remove parentheses.

$y = \sqrt[3]{0}$

Rewrite $0$ as $0^{3}$ .

$y = \sqrt[3]{0^{3}}$

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

$y = 0$

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

Find the Vertical and Horizontal Intercept(s) f(x) = cube root of x

Related Questions

Support LCMGCF.com by disabling your adblocker.