The problem asks to identify the transformations applied to the parent function $h(x)$ to obtain the function $f(x) = 8h(-x) - 7$. The transformations to be identified are reflections, stretches/compressions, vertical shifts, and horizontal shifts.

1. Problem Description

The problem asks to identify the transformations applied to the parent function $h(x)$ to obtain the function $f(x) = 8h(-x) - 7$. The transformations to be identified are reflections, stretches/compressions, vertical shifts, and horizontal shifts.

2. Solution Steps

The given function is $f(x) = 8h(-x) - 7$. We need to identify the transformations applied to $h(x)$.

a) Reflections:

The argument of $h$ is $-x$. This means there is a reflection about the y-axis.

b) Stretches/Compressions:

The function $h(-x)$ is multiplied by 8, so there is a vertical stretch by a factor of

8.

c) Vertical Shifts:

There is a $-7$ at the end, so there is a vertical shift down by 7 units.

d) Horizontal Shifts:

There are no horizontal shifts.

3. Final Answer

a) Reflection about the y-axis.

b) Vertical stretch by a factor of

8. c) Vertical shift down by 7 units.

d) No horizontal shifts.