Question

Describe the Transformations that results in h(x)= f(-x) +5(4 points)
The function f(x) is
and then

Answer 1

To describe the transformations that result in the function \( h(x) = f(-x) + 5 \) based on the original function \( f(x) \), we can break down the transformations step by step:

1. **Reflection**: The term \( f(-x) \) represents a reflection of the function \( f(x) \) across the \( y \)-axis. This means that for every point \( (x, f(x)) \) on the original graph of \( f(x) \), the new point on the graph of \( f(-x) \) will be \( (-x, f(x)) \).

2. **Vertical Shift**: The \( + 5 \) in \( h(x) = f(-x) + 5 \) indicates a vertical shift of the entire graph of \( f(-x) \) upwards by 5 units. This means that every point on the graph of \( f(-x) \) will be moved up 5 units.

Combining these two transformations, we have:
- First, reflect the function \( f(x) \) across the \( y \)-axis to get \( f(-x) \).
- Then, take the resulting graph and shift it vertically upwards by 5 units to obtain \( h(x) \).

In summary, the transformations that result in \( h(x) = f(-x) + 5 \) are:
1. Reflection across the \( y \)-axis.
2. Vertical shift upwards by 5 units.