Evaluate the piecewise function at the given values of the independent variable \( f(x)=\left\{\begin{array}{ll}3 x+5 & \text { if } x<0 \\ 3 x+6 & \text { if } x \geq 0\end{array}\right. \) (a) \( f(-4) \) (b) \( f(0) \) (c) \( f(2) \) \( \begin{array}{l}\text { (a) } f(-4)=\square \\ \text { (b) } f(0)=\square \\ \text { (c) } f(2)=\square\end{array} \)

To evaluate the piecewise function \( f(x) \), we need to check the conditions for each value of \( x \): (a) For \( f(-4) \): Since \(-4 < 0\), we use the first case of the function: \[ f(-4) = 3(-4) + 5 = -12 + 5 = -7 \] So, \( f(-4) = -7 \). (b) For \( f(0) \): Since \(0 \geq 0\), we use the second case of the function: \[ f(0) = 3(0) + 6 = 0 + 6 = 6 \] So, \( f(0) = 6 \). (c) For \( f(2) \): Since \(2 \geq 0\), we again use the second case of the function: \[ f(2) = 3(2) + 6 = 6 + 6 = 12 \] So, \( f(2) = 12 \). Putting it all together: \[ \begin{array}{l} \text { (a) } f(-4)=-7 \\ \text { (b) } f(0)=6 \\ \text { (c) } f(2)=12 \end{array} \]