(a) Sketch \( y = f(x – 4) \):

The transformation \( y = f(x – 4) \) represents a horizontal translation of the graph of \( y = f(x) \) to the right by 4 units. Each point \( (x, y) \) on the original graph is mapped to \( (x + 4, y) \). The points \( A \), \( B \), \( C \), and \( D \) on the graph of \( y = f(x) \) are shifted 4 units to the right, preserving their \( y \)-coordinates.

Answer: The graph of \( y = f(x – 4) \) is as shown above, with the images of points \( A \), \( B \), \( C \), and \( D \) shifted 4 units to the right.

(b) Sketch \( y = f(-x) \):

The transformation \( y = f(-x) \) represents a reflection of the graph of \( y = f(x) \) across the \( y \)-axis. Each point \( (x, y) \) on the original graph is mapped to \( (-x, y) \). The points \( A \), \( B \), \( C \), and \( D \) are reflected across the \( y \)-axis, preserving their \( y \)-coordinates but negating their \( x \)-coordinates.

Answer: The graph of \( y = f(-x) \) is as shown above, with the images of points \( A \), \( B \), \( C \), and \( D \) reflected across the \( y \)-axis.