Precalculus Examples

$f (x) = x^{4} - 6$

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

$0 = x^{4} - 6$

Solve the equation.

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Rewrite the equation as $x^{4} - 6 = 0$ .

$x^{4} - 6 = 0$

Add $6$ to both sides of the equation.

$x^{4} = 6$

Take the $4th$ root of both sides of the $equation$ to eliminate the exponent on the left side.

$x = \pm \sqrt[4]{6}$

The complete solution is the result of both the positive and negative portions of the solution.

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First, use the positive value of the $\pm$ to find the first solution.

$x = \sqrt[4]{6}$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - \sqrt[4]{6}$

The complete solution is the result of both the positive and negative portions of the solution.

$x = \sqrt[4]{6}, - \sqrt[4]{6}$

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

$y = {(0)}^{4} - 6$

Simplify ${(0)}^{4} - 6$ .

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

$y = 0 - 6$

Subtract $6$ from $0$ .

$y = - 6$

These are the $x$ and $y$ intercepts of the equation $y = x^{4} - 6$ .

x-intercept: $(\sqrt[4]{6}, 0), (- \sqrt[4]{6}, 0)$

y-intercept: $(0, - 6)$

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