\( f(x)=\left\{\begin{array}{ll}|x| \text { if } x<0 & \text { a. Find } f(-5), f(0) \text {, and } f(7) \text {. } \\ 5 \text { if } x=0 & \text { b. Sketch the graph of the piecewise-defined function. } \\ \sqrt{x} \text { if } x>0 & \text { c. Determine the domain of } f .\end{array}\right. \)

To find \( f(-5) \), since \( -5 < 0 \), we use the first piece of the function: \( f(-5) = |-5| = 5 \). For \( f(0) \), the value is defined as \( 5 \) because it’s explicitly stated for \( x=0 \). Lastly, for \( f(7) \), since \( 7 > 0 \), we use the third piece: \( f(7) = \sqrt{7} \), which is approximately \( 2.64575 \). To sketch the graph of the function, start by plotting the line for \( |x| \) in the negative region (where \( x < 0 \)), which goes from the origin downwards as a straight line (a triangle shape till \( (-5, 5) \)). At \( x=0 \), plot a point at \( (0, 5) \). For \( x > 0 \), graph \( \sqrt{x} \), which starts at the origin and curves upwards. Make sure to connect the regions smoothly at the defined points! The domain of \( f \) includes all \( x \) values where the function is defined. Here, it encompasses all real numbers, so the domain is \( (-\infty, \infty) \).