The point \( (4,64) \) is on the graph of \( f(x)=x^{3} \). What is the point \( (4,64) \) shifted to when \( g(x)=f(x)+8 \) ? (1 point) \( (-4,72) \) \( (4,58) \) \( (4,72) \) \( (72,4) \)

When we have the function \( g(x) = f(x) + 8 \), it means that we are shifting the entire graph of \( f(x) \) upwards by 8 units. Therefore, if the point \( (4, 64) \) is on the graph of \( f(x) \), then to find the corresponding point on the graph of \( g(x) \), we simply add 8 to the y-coordinate of the point. So, from \( (4, 64) \), we calculate the new y-coordinate: \[ 64 + 8 = 72 \] Thus, the new point is \( (4, 72) \). The correct answer is \( (4,72) \).