Find the x and y Intercepts f(x)=x^4-6

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

Find the x-intercepts.

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

$0 = x^{4} - 6$

Solve the equation.

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.

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.

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

x-intercept(s) in point form.

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

Find the y-intercepts.

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

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

Solve the equation.

Remove parentheses.

$y = 0^{4} - 6$

Remove parentheses.

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

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

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

$y = 0 - 6$

Subtract $6$ from $0$ .

$y = - 6$

y-intercept(s) in point form.

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

List the intersections.

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

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