Describe the transformation that occurs on a graph when changing an equation from f(x)=-|x| to -|x| +4

Question

Shifts vertically down 4 units
Shifts horizontally to the right 4 units
Shifts horizontally to the left 4 units
Shifts vertically up 4 units

Answer 1

The transformation involved when changing the equation from \( f(x) = -|x| \) to \( f(x) = -|x| + 4 \) is a vertical shift.

Specifically:

• The addition of +4 to the equation \( -|x| \) moves the graph upward by 4 units.

Thus, the correct description of the transformation is:

Shifts vertically up 4 units.

To clarify, the original function \( -|x| \) is reflected over the x-axis (due to the negative sign) and the new function \( -|x| + 4 \) results in the entire graph of \( -|x| \) being lifted 4 units higher on the y-axis.