Find the indicated intercept(s) of the graph of the function.2133:2139
-$$x \text {-intercepts of } f ( x ) = \frac { x ^ { 3 } - 27 } { x ^ { 2 } - 25 }$$
A) (-3, 0), (3, 0)
B) (5, 0)
C) (- 27, 0)
D) (3, 0)

Question

Quizplus · Accepted Answer

To find the x-intercepts of the given function, we set $f(x) = 0$ and solve for $x$. This gives us the equation $\frac{x^3 - 27}{x^2 - 25} = 0$. The numerator $x^3 - 27 = 0$ when $x^3 = 27$, which gives $x = 3$. The denominator $x^2 - 25$ does not affect the x-intercepts directly but indicates points where the function is undefined (at $x = \pm5$). Therefore, the only x-intercept is at $x = 3$, or the point (3, 0).

Find the Indicated Intercept(s) of the Graph of the Function x-intercepts of f(x)=x3−27x2−25x \text {-intercepts of } f ( x ) = \frac { x ^ { 3 } - 27 } { x ^ { 2 } - 25 }x-intercepts of f(x)=x2−25x3−27​

Find the Indicated Intercept(s) of the Graph of the Function $x \text {-intercepts of } f ( x ) = \frac { x ^ { 3 } - 27 } { x ^ { 2 } - 25 }$