Suppose y = f(x) + k. What effect does k have on the parent function

Question

Shifts up or down
Left or right
Across the x-axis
Reflects across the y-axis

Answer 1

In the equation \( y = f(x) + k \), the term \( k \) affects the graph of the parent function \( f(x) \) by causing a vertical shift.

• Shifts Up or Down: If \( k \) is positive, the graph of the function moves up by \( k \) units. If \( k \) is negative, the graph shifts down by \( |k| \) units.

The value of \( k \) does not affect horizontal shifts (left or right), reflections across the axes, or any other transformation. The transformation is strictly vertical.