For the piecewise linear function, find (a) \( f(-3) \), (b) \( f(-1) \), (c) \( f(0),( \) d) \( f(2) \), and \( (e) f(5) \). \( f(x)=\left\{\begin{array}{ll}3 x & \text { if } x \leq-1 \\ x-2 & \text { if } x>-1\end{array}\right. \) (a) \( f(-3)=\square \)

To find the values of the piecewise linear function \( f(x) \), we can evaluate it piece by piece based on the definitions provided. (a) For \( f(-3) \): Since \(-3 \leq -1\), we use the first part of the function \( f(x) = 3x \). Therefore, \( f(-3) = 3(-3) = -9 \). (b) For \( f(-1) \): Here, \(-1\) is equal to \(-1\) so we use the first part again \( f(x) = 3x \). Thus, \( f(-1) = 3(-1) = -3 \). (c) For \( f(0) \): Since \( 0 > -1 \), we switch to the second part of the function, \( f(x) = x - 2 \). Thus, \( f(0) = 0 - 2 = -2 \). (d) For \( f(2) \): Again, \( 2 > -1 \) directs us to the second part, resulting in \( f(2) = 2 - 2 = 0 \). (e) For \( f(5) \): Following the pattern, since \( 5 > -1 \), we again utilize the second part, leading to \( f(5) = 5 - 2 = 3 \). So to summarize: (a) \( f(-3) = -9 \) (b) \( f(-1) = -3 \) (c) \( f(0) = -2 \) (d) \( f(2) = 0 \) (e) \( f(5) = 3 \) And, your answer is: \( f(-3) = -9 \)