Vertical shift

Definition

A vertical shift is a transformation that moves a graph up or down in the coordinate plane by adding or subtracting a constant to the function's output. It does not affect the shape of the graph, only its position.

5 Must Know Facts For Your Next Test

1. The vertical shift is determined by the constant $k$ in $f(x) + k$ or $f(x) - k$.
2. A positive $k$ value shifts the graph upward, while a negative $k$ value shifts it downward.
3. Vertical shifts do not change the x-intercepts of the function.
4. In exponential functions, vertical shifts can affect asymptotes but not their general shape.
5. For logarithmic functions, vertical shifts move the entire graph up or down without changing its domain.

Review Questions

• How does adding a positive constant to a function's output affect its graph?
• What happens to an exponential function's asymptote when it undergoes a vertical shift?
• Does a vertical shift alter the x-intercepts of a linear function?

Related terms

Horizontal Shift:

A horizontal shift moves a graph left or right by adding or subtracting a constant to the input of the function.

Reflection:

A reflection flips the graph over a specified axis, such as reflecting it over the x-axis by multiplying the output by -1.

Scaling: $Scaling$ involves stretching or compressing the graph vertically or horizontally by multiplying either the input or output by a constant factor.