Question

complete the description of the piecewise function graphed below.
f(x) =
{ if -6 ≤ x ≤ -3
{ if -3 < x ≤ 2
{ if 2 < x ≤ 6

Answer 1

To complete the description of the piecewise function, you’ll need to provide the definitions for the function \( f(x) \) within the specified intervals. Since I cannot see the graph you mentioned, I will provide a template for a piecewise function, and you can fill in the appropriate definitions based on the graph you have:

\[
f(x) =
\begin{cases}
f_1(x) & \text{if } -6 \leq x \leq -3 \\
f_2(x) & \text{if } -3 < x \leq 2 \\
f_3(x) & \text{if } 2 < x \leq 6
\end{cases}
\]

Where \( f_1(x) \), \( f_2(x) \), and \( f_3(x) \) are the equations or values corresponding to each interval.

For example, if you have a linear function in the first interval, a quadratic function in the second, and a constant value in the third, it might look like this:

\[
f(x) =
\begin{cases}
2x + 4 & \text{if } -6 \leq x \leq -3 \\
-x^2 + 4 & \text{if } -3 < x \leq 2 \\
3 & \text{if } 2 < x \leq 6
\end{cases}
\]

Please replace \( f_1(x) \), \( f_2(x) \), and \( f_3(x) \) with the appropriate functions based on the graph you are looking at to complete the description of the piecewise function.