Find the x- and y-intercepts of f.
-$$f ( x ) = 3 x - x ^ { 3 }$$
A) $x$-intercepts: $0 , - 3$; $y$-intercept: 0
B) $x$-intercepts: $0 , \sqrt { 3 } , - \sqrt { 3 } ; y$-intercept: 3
C) $x$-intercepts: $0 , \sqrt { 3 } , - \sqrt { 3 } ; y$-intercept: 0
D) x-intercepts: $0 , - 3 ; y$-intercept: 3

Question

Quizplus · Accepted Answer

To find the x-intercepts, set $f(x) = 0$: $0 = 3x - x^3$. Factoring gives $x(3 - x^2) = 0$, leading to $x = 0, \pm\sqrt{3}$. For the y-intercept, set $x = 0$: $f(0) = 3(0) - (0)^3 = 0$.

Find the X- and Y-Intercepts of F f(x)=3x−x3f ( x ) = 3 x - x ^ { 3 }f(x)=3x−x3

Find the X- and Y-Intercepts of F $f ( x ) = 3 x - x ^ { 3 }$