The graph of a function $$ f $$ is shown to the right. Use the graph to find the following. $$ f(-1)=-4 $$ Choose the correct domain. A. $$ (-5,3) $$ B. $$ (-6,-2) $$ C. $$ (-10,10) $$ D. $$ (-\infty, \infty) $$ What is the set of all $$ x $$-values such that $$ f(x)=-5 $$ ? A. $$ \varnothing $$ B. $$ \{-3\} $$ C. $$ (-5,3) $$

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To find the domain of the function $$ f $$ based on the given graph, we need to identify the set of all $$ x $$-values for which the function is defined.

Given that $$ f(-1) = -4 $$, we can see from the graph that the function is defined for all real numbers. Therefore, the domain of the function $$ f $$ is all real numbers, which can be represented as $$ (-\infty, \infty) $$.

Now, to find the set of all $$ x $$-values such that $$ f(x) = -5 $$, we need to look for the points on the graph where the function value is -5.

From the graph, we can see that there is no point where the function value is -5. Therefore, the set of all $$ x $$-values such that $$ f(x) = -5 $$ is the empty set, denoted as $$ \varnothing $$.

So, the correct answers are:
A. $$ (-5,3) $$ is not the correct domain.
B. $$ (-6,-2) $$ is not the correct domain.
C. $$ (-10,10) $$ is not the correct domain.
D. $$ (-\infty, \infty) $$ is the correct domain.
A. $$ \varnothing $$ is the correct set of all $$ x $$-values such that $$ f(x) = -5 $$.
The domain of the function $$ f $$ is all real numbers, so the correct choice is D. $$ (-\infty, \infty) $$. There are no $$ x $$-values where $$ f(x) = -5 $$, so the correct choice is A. $$ \varnothing $$.

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