Find the x and y Intercepts f(x)=x^5-1+3x^4

$f (x) = x^{5} - 1 + 3 x^{4}$

Find the x-intercepts.

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

$0 = x^{5} - 1 + 3 x^{4}$

Solve the equation.

Remove parentheses.

$0 = x^{5} - 1 + 3 x^{4}$

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

$x \approx - 2.98744548, - 0.82328375, 0.72005023$

x-intercept(s) in point form.

x-intercept(s): $(- 2.98744548, 0), (- 0.82328375, 0), (0.72005023, 0)$

Find the y-intercepts.

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

$y = {(0)}^{5} - 1 + 3 {(0)}^{4}$

Solve the equation.

Remove parentheses.

$y = 0^{5} - 1 + 3 {(0)}^{4}$

Remove parentheses.

$y = 0^{5} - 1 + 3 \cdot 0^{4}$

Remove parentheses.

$y = {(0)}^{5} - 1 + 3 {(0)}^{4}$

Simplify ${(0)}^{5} - 1 + 3 {(0)}^{4}$ .

Simplify each term.

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

$y = 0 - 1 + 3 {(0)}^{4}$

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

$y = 0 - 1 + 3 \cdot 0$

Multiply $3$ by $0$ .

$y = 0 - 1 + 0$

Simplify by adding and subtracting.

Subtract $1$ from $0$ .

$y = - 1 + 0$

Add $- 1$ and $0$ .

$y = - 1$

y-intercept(s) in point form.

y-intercept(s): $(0, - 1)$

List the intersections.

x-intercept(s): $(- 2.98744548, 0), (- 0.82328375, 0), (0.72005023, 0)$

y-intercept(s): $(0, - 1)$