To find [tex]\( f(-3) \)[/tex] for the given piecewise function, we need to determine which part of the function to use based on the value of [tex]\( x \)[/tex].
The piecewise function is defined as:
[tex]\[ f(x) = \begin{cases}
2x + 2 & \text{if } x \leq 0 \\
-\frac{4}{3}x + 4 & \text{if } x > 0
\end{cases} \][/tex]
Given [tex]\( x = -3 \)[/tex]:
1. First, we need to determine which part of the piecewise function applies to [tex]\( x = -3 \)[/tex].
2. Since [tex]\(-3 \leq 0\)[/tex], we use the first part of the function [tex]\( f(x) = 2x + 2 \)[/tex].
Now, we substitute [tex]\( x = -3 \)[/tex] into the first part:
[tex]\[ f(-3) = 2(-3) + 2 \][/tex]
Calculate the expression step by step:
[tex]\[ f(-3) = 2 \cdot (-3) + 2 \][/tex]
[tex]\[ f(-3) = -6 + 2 \][/tex]
[tex]\[ f(-3) = -4 \][/tex]
Therefore, the value of [tex]\( f(-3) \)[/tex] is:
[tex]\[ f(-3) = -4 \][/tex]
