To evaluate the piecewise-defined function \( f(x) \) at \( x = -3 \), we need to determine which piece of the function to use.
Given the function:
[tex]\[
f(x) = \left\{\begin{array}{ll}
5x - 1 & \text{if} \, x < -3 \\
-3x - 1 & \text{if} \, x \geq -3
\end{array}\right.
\][/tex]
We see that \( x = -3 \) falls into the condition \( x \geq -3 \). Therefore, we will use the second piece of the function, which is \( -3x - 1 \).
Now, substituting \( x = -3 \) into this equation:
[tex]\[
f(-3) = -3(-3) - 1
\][/tex]
First, compute the multiplication part:
[tex]\[
-3 \times -3 = 9
\][/tex]
Next, subtract 1 from the result:
[tex]\[
9 - 1 = 8
\][/tex]
Thus, the value of \( f(-3) \) is:
[tex]\[
f(-3) = 8
\][/tex]
