Given the graph of \( y=f(x) \), if \( a \) is a positive real number such that \( a>1 \), then which of the following statements best describes the graph of \( y=\operatorname{af}(x) \) ? Choose the correct answer. A. The graph of \( y=a f(x) \) is a horizontal stretch of the graph of \( y=f(x) \). B. The graph of \( y=a f(x) \) is a vertical compression of the graph of \( y=f(x) \). C. The graph of \( y=a f(x) \) is a horizontal compression of the graph of \( y=f(x) \). D. The graph of \( y=a f(x) \) is a vertical stretch of the graph of \( y=f(x) \).

To analyze the transformation represented by \( y = a f(x) \) where \( a > 1 \), we need to understand how the graph of the function \( f(x) \) is affected by multiplying it by a constant \( a \). 1. **Vertical Stretch/Compression**: When you multiply the output of a function \( f(x) \) by a constant \( a \): - If \( a > 1 \), the graph is stretched vertically. This means that for each \( x \), the value of \( y \) is increased by a factor of \( a \). Points on the graph move away from the x-axis. - If \( 0 < a < 1 \), the graph would be compressed vertically. 2. **Horizontal Stretch/Compression**: These transformations occur when you multiply the input \( x \) by a constant: - If you have \( y = f(bx) \) where \( b > 1 \), the graph is compressed horizontally. - If \( 0 < b < 1 \), the graph is stretched horizontally. In this case, since we are looking at \( y = a f(x) \) with \( a > 1 \), the correct description is that the graph of \( y = a f(x) \) is a vertical stretch of the graph of \( y = f(x) \). Thus, the correct answer is: **D. The graph of \( y = a f(x) \) is a vertical stretch of the graph of \( y = f(x) \).**