Algebra Examples

$f (x) = \sqrt[3]{x + 1}$

Step 1

Find the x-intercepts.

Tap for more steps...

Step 1.1

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

$0 = \sqrt[3]{x + 1}$

Step 1.2

Solve the equation.

Tap for more steps...

Step 1.2.1

Rewrite the equation as $\sqrt[3]{x + 1} = 0$ .

$\sqrt[3]{x + 1} = 0$

Step 1.2.2

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

${\sqrt[3]{x + 1}}^{3} = 0^{3}$

Step 1.2.3

Simplify each side of the equation.

Tap for more steps...

Step 1.2.3.1

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

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

Step 1.2.3.2

Simplify the left side.

Tap for more steps...

Step 1.2.3.2.1

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

Tap for more steps...

Step 1.2.3.2.1.1

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

Tap for more steps...

Step 1.2.3.2.1.1.1

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

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

Step 1.2.3.2.1.1.2

Cancel the common factor of $3$ .

Tap for more steps...

Step 1.2.3.2.1.1.2.1

Cancel the common factor.

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

Step 1.2.3.2.1.1.2.2

Rewrite the expression.

${(x + 1)}^{1} = 0^{3}$

Step 1.2.3.2.1.2

Simplify.

$x + 1 = 0^{3}$

Step 1.2.3.3

Simplify the right side.

Tap for more steps...

Step 1.2.3.3.1

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

$x + 1 = 0$

Step 1.2.4

Subtract $1$ from both sides of the equation.

$x = - 1$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(- 1, 0)$

Step 2

Find the y-intercepts.

Tap for more steps...

Step 2.1

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

$y = \sqrt[3]{(0) + 1}$

Step 2.2

Simplify $\sqrt[3]{(0) + 1}$ .

Tap for more steps...

Step 2.2.1

Add $0$ and $1$ .

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

Step 2.2.2

Any root of $1$ is $1$ .

$y = 1$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, 1)$

Step 3

List the intersections.

x-intercept(s): $(- 1, 0)$

y-intercept(s): $(0, 1)$

Step 4