Vertical shift

Definition

A vertical shift is a transformation that moves a graph up or down by adding or subtracting a constant to the function's output. This does not change the shape of the graph, only its position along the y-axis.

5 Must Know Facts For Your Next Test

1. A vertical shift of $f(x)$ by $c$ units is represented as $f(x) + c$.
2. If $c$ is positive, the graph shifts upward; if $c$ is negative, it shifts downward.
3. Vertical shifts do not affect the x-coordinates of points on the graph, only the y-coordinates.
4. The amplitude and period of periodic functions like sine and cosine remain unchanged with vertical shifts.
5. Vertical shifts can be used in combination with other transformations such as horizontal shifts, reflections, and stretches.

Review Questions

• How does adding a positive constant to a function's equation affect its graph?
• What happens to the coordinates of points on a function's graph when it undergoes a vertical shift?
• Can a vertical shift alter the period of a periodic function like sine or cosine?

Related terms

Horizontal Shift: A transformation that moves the graph left or right by adding or subtracting a constant to the function’s input.

Amplitude: The maximum absolute value of displacement from zero in periodic functions like sine and cosine.

Period: \text{The length of one complete cycle in periodic functions like sine and cosine.}