To solve for [tex]\( f(-3) \)[/tex] in the given piecewise function, let's follow these steps:
We are given the piecewise function:
[tex]\[
\begin{cases}
y = -2x + 5 & \text{if } x < 4 \\
y = \frac{x}{4} - 4 & \text{if } x \geq 4
\end{cases}
\][/tex]
Step 1: Determine which part of the piecewise function to use.
Since we need to find [tex]\( f(-3) \)[/tex], we substitute [tex]\( x = -3 \)[/tex].
Step 2: Identify the relevant piece of the function.
We check the condition [tex]\( x < 4 \)[/tex]. Since [tex]\( -3 < 4 \)[/tex] is true, we use the equation [tex]\( y = -2x + 5 \)[/tex].
Step 3: Substitute [tex]\( x = -3 \)[/tex] into the appropriate piece of the function.
[tex]\[ y = -2(-3) + 5 \][/tex]
Step 4: Calculate the result step-by-step.
[tex]\[
-2(-3) + 5 = 6 + 5 = 11
\][/tex]
Thus, the value of [tex]\( f(-3) \)[/tex] is:
[tex]\[
f(-3) = 11
\][/tex]
Therefore, [tex]\( f(-3) = 11 \)[/tex].
