Describe the transformations that results in h(x) =f(-x)+5

Question

The function f(x) is ______ and then ______

Answer 1

To describe the transformations that result in \( h(x) = f(-x) + 5 \), we can break it down into two main transformations applied to the function \( f(x) \).

1. Horizontal Reflection: The transformation from \( f(x) \) to \( f(-x) \) represents a reflection across the y-axis. This means that for every input \( x \), the output of the function is taken at the opposite point, thus flipping the graph of \( f(x) \) horizontally.

2. Vertical Shift: The transformation \( f(-x) + 5 \) represents a vertical shift of the entire function \( f(-x) \) upward by 5 units. This means that after reflecting \( f(x) \) across the y-axis, we then move each point of the resulting graph up 5 units.

Putting it all together, we can say:

The function \( f(x) \) is reflected across the y-axis and then shifted upward by 5 units.