Finite Math Examples

$f (x) = \frac{3}{2} x^{4}$

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 $x$ .

$0 = \frac{3}{2} x^{4}$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $\frac{3}{2} x^{4} = 0$ .

$\frac{3}{2} x^{4} = 0$

Step 1.2.2

Multiply both sides of the equation by $\frac{2}{3}$ .

$\frac{2}{3} (\frac{3}{2} x^{4}) = \frac{2}{3} \cdot 0$

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 $\frac{2}{3} (\frac{3}{2} x^{4})$ .

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Step 1.2.3.1.1.1

Combine $\frac{3}{2}$ and $x^{4}$ .

$\frac{2}{3} \cdot \frac{3 x^{4}}{2} = \frac{2}{3} \cdot 0$

Step 1.2.3.1.1.2

Combine.

$\frac{2 (3 x^{4})}{3 \cdot 2} = \frac{2}{3} \cdot 0$

Step 1.2.3.1.1.3

Cancel the common factor of $2$ .

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Step 1.2.3.1.1.3.1

Cancel the common factor.

$\frac{2 (3 x^{4})}{3 \cdot 2} = \frac{2}{3} \cdot 0$

Step 1.2.3.1.1.3.2

Rewrite the expression.

$\frac{3 x^{4}}{3} = \frac{2}{3} \cdot 0$

Step 1.2.3.1.1.4

Cancel the common factor of $3$ .

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Step 1.2.3.1.1.4.1

Cancel the common factor.

$\frac{3 x^{4}}{3} = \frac{2}{3} \cdot 0$

Step 1.2.3.1.1.4.2

Divide $x^{4}$ by $1$ .

$x^{4} = \frac{2}{3} \cdot 0$

Step 1.2.3.2

Simplify the right side.

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Step 1.2.3.2.1

Multiply $\frac{2}{3}$ by $0$ .

$x^{4} = 0$

Step 1.2.4

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

$x = \pm \sqrt[4]{0}$

Step 1.2.5

Simplify $\pm \sqrt[4]{0}$ .

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Step 1.2.5.1

Rewrite $0$ as $0^{4}$ .

$x = \pm \sqrt[4]{0^{4}}$

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 $y$ .

$y = \frac{3}{2} \cdot {(0)}^{4}$

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

$y = \frac{3}{2} \cdot 0^{4}$

Step 2.2.2

Remove parentheses.

$y = \frac{3}{2} \cdot {(0)}^{4}$

Step 2.2.3

Simplify $\frac{3}{2} \cdot {(0)}^{4}$ .

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Step 2.2.3.1

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

$y = \frac{3}{2} \cdot 0$

Step 2.2.3.2

Multiply $\frac{3}{2}$ by $0$ .

$y = 0$

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