Finite Math Examples

$x^{3} - 3 x - 8$

Step 1

Write $x^{3} - 3 x - 8$ as an equation.

$y = x^{3} - 3 x - 8$

Step 2

Find the x-intercepts.

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Step 2.1

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

$0 = x^{3} - 3 x - 8$

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

$0 = x^{3} - 3 x - 8$

Step 2.2.2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx 2.4920333$

Step 2.3

x-intercept(s) in point form.

x-intercept(s): $(2.4920333, 0)$

Step 3

Find the y-intercepts.

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Step 3.1

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

$y = {(0)}^{3} - 3 \cdot 0 - 8$

Step 3.2

Solve the equation.

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Step 3.2.1

Remove parentheses.

$y = 0^{3} - 3 \cdot 0 - 8$

Step 3.2.2

Remove parentheses.

$y = {(0)}^{3} - 3 \cdot 0 - 8$

Step 3.2.3

Simplify ${(0)}^{3} - 3 \cdot 0 - 8$ .

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Step 3.2.3.1

Simplify each term.

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Step 3.2.3.1.1

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

$y = 0 - 3 \cdot 0 - 8$

Step 3.2.3.1.2

Multiply $- 3$ by $0$ .

$y = 0 + 0 - 8$

Step 3.2.3.2

Simplify by adding and subtracting.

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Step 3.2.3.2.1

Add $0$ and $0$ .

$y = 0 - 8$

Step 3.2.3.2.2

Subtract $8$ from $0$ .

$y = - 8$

Step 3.3

y-intercept(s) in point form.

y-intercept(s): $(0, - 8)$

Step 4

List the intersections.

x-intercept(s): $(2.4920333, 0)$

y-intercept(s): $(0, - 8)$

Step 5