$$ \text { Find the domain and the } x \text { - and } y \text {-intercepts of } f(x) \text {. Then graph the function. } $$ $$ f(x)=\frac{x-2}{(x+4)^{2}} $$ What is the domain of $$ f(x) $$ ? A. $$ (-\infty, 2) \cup(2, \infty) $$ B. $$ (-\infty, \infty) $$ C. $$ (-\infty,-4) \cup(-4, \infty) $$

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UpStudy AI · Accepted Answer

The function is given by

$$
f(x)=\frac{x-2}{(x+4)^{2}}.
$$

To find the domain, we need to identify values of $$ x $$ where the function is defined. Since the only potential issue is division by zero, we set the denominator equal to zero:

$$
(x+4)^{2}=0.
$$

Taking the square root of both sides gives:

$$
x+4=0 \quad \Longrightarrow \quad x=-4.
$$

Thus, the function is undefined at $$ x=-4 $$.

The domain of $$ f(x) $$ is all real numbers except $$ x=-4 $$, which in interval notation is

$$
(-\infty, -4) \cup (-4,\infty).
$$

Comparing with the provided options, the correct answer is:

C. $$ (-\infty,-4) \cup(-4, \infty) $$.
The domain of $$ f(x) $$ is all real numbers except $$ x = -4 $$, which is $$ (-\infty, -4) \cup (-4, \infty) $$.

What is the domain of ?
A.
B.
C.

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