Find the x- and y-intercepts of f.
-$$f ( x ) = - x ^ { 2 } ( x + 6 ) \left( x ^ { 2 } + 1 \right)$$
A)x-intercepts: -6, -1, 0; y-intercept: 6
B)x-intercepts: -6, -1, 0; y-intercept: -6
C)x-intercepts: -6, 0; y-intercept: 0
D)x-intercepts: -6, -1, 0, 1; y-intercept: 0

Question

Quizplus · Accepted Answer

To find the x-intercepts, set $f(x) = 0$:$$-x^2(x + 6)(x^2 + 1) = 0$$This equation is satisfied when $x = 0$ and $x = -6$. The term $x^2 + 1$ cannot be zero because $x^2$ is always non-negative, making $x^2 + 1 > 0$ for all real numbers $x$. Therefore, the x-intercepts are -6 and 0.To find the y-intercept, set $x = 0$:$$f(0) = -0^2(0 + 6)(0^2 + 1) = 0$$Thus, the y-intercept is 0.

Find the X- and Y-Intercepts of F f(x)=−x2(x+6)(x2+1)f ( x ) = - x ^ { 2 } ( x + 6 ) \left( x ^ { 2 } + 1 \right)f(x)=−x2(x+6)(x2+1)

Find the X- and Y-Intercepts of F $f ( x ) = - x ^ { 2 } ( x + 6 ) \left( x ^ { 2 } + 1 \right)$