The domain of the piecewise function is $(-\infty, \infty)$.
a. Graph the function.
b. Use your graph to determine the function's range.
\[
f(x)=\left\{\begin{array}{lll}
x+3 & \text { if } & x< -4 \\
x-3 & \text { if } & x \geq-4
\end{array}\right.
\]
a. Choose the correct graph below.
A.
B.
b. What is the range of the entire piecewise function? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.
A. The range does not have any isolated values. It can be described by $\square$. (Type your answer in interval notation.)
B. The range has at least one isolated value. It can be described as the union of the interval(s) $\square$ and the set \{\} . (Use a comma to separate answers as needed.)
c. The range consists exclusively of one or more isolated values. It can be described as \{\} . (Use a comma to separate answers as needed.)
Answer
Final Answer: The range of the piecewise function is \(\boxed{(-\infty, -1] \cup [-7, \infty)}\).
Step 1 ：The function is defined as \(f(x) = x + 3\) for \(x < -4\) and \(f(x) = x - 3\) for \(x \geq -4\).
Step 2 ：For the first part of the function, as \(x\) approaches \(-\infty\), \(f(x)\) also approaches \(-\infty\). As \(x\) approaches \(-4\), \(f(x)\) approaches \(-1\).
Step 3 ：For the second part of the function, as \(x\) approaches \(-4\), \(f(x)\) approaches \(-7\). As \(x\) approaches \(\infty\), \(f(x)\) also approaches \(\infty\).
Step 4 ：Therefore, the range of the function is \((-\infty, -1] \cup [-7, \infty)\).
Step 5 ：Final Answer: The range of the piecewise function is \(\boxed{(-\infty, -1] \cup [-7, \infty)}\).
