Questions: Write a function g whose graph represents the indicated transformation of the graph of f g(x)=

Solution Steps

The original function \( f(x) \) appears to be \( f(x) = |x| \), which is the absolute value function.

The graph shows a reflection over the x-axis and a vertical shift downward by 2 units. This means the transformation applied to \( f(x) \) is:

1. Reflect over the x-axis: \( -f(x) \)
2. Shift downward by 2 units: \( -f(x) - 2 \)

Apply the transformations to the original function \( f(x) = |x| \):

1. Reflect over the x-axis: \( -|x| \)
2. Shift downward by 2 units: \( -|x| - 2 \)

Final Answer