Precalculus Examples

$y = x^{3} + 4$

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 $x$ .

$0 = x^{3} + 4$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $x^{3} + 4 = 0$ .

$x^{3} + 4 = 0$

Step 1.2.2

Subtract $4$ from both sides of the equation.

$x^{3} = - 4$

Step 1.2.3

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

$x = \sqrt[3]{- 4}$

Step 1.2.4

Simplify $\sqrt[3]{- 4}$ .

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Step 1.2.4.1

Rewrite $- 4$ as ${(- 1)}^{3} \cdot 4$ .

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Step 1.2.4.1.1

Rewrite $- 4$ as $- 1 (4)$ .

$x = \sqrt[3]{- 1 (4)}$

Step 1.2.4.1.2

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

$x = \sqrt[3]{{(- 1)}^{3} \cdot 4}$

Step 1.2.4.2

Pull terms out from under the radical.

$x = - 1 \sqrt[3]{4}$

Step 1.2.4.3

Rewrite $- 1 \sqrt[3]{4}$ as $- \sqrt[3]{4}$ .

$x = - \sqrt[3]{4}$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(- \sqrt[3]{4}, 0)$

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 $y$ .

$y = {(0)}^{3} + 4$

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

$y = 0^{3} + 4$

Step 2.2.2

Remove parentheses.

$y = {(0)}^{3} + 4$

Step 2.2.3

Simplify ${(0)}^{3} + 4$ .

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Step 2.2.3.1

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

$y = 0 + 4$

Step 2.2.3.2

Add $0$ and $4$ .

$y = 4$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, 4)$

Step 3

List the intersections.

x-intercept(s): $(- \sqrt[3]{4}, 0)$

y-intercept(s): $(0, 4)$

Step 4