Vertical Shift
See It in Action
Two examples of the idea done right—and one common look-alike that is not right.
EXAMPLE
EXAMPLE
NON-EXAMPLE
Definition
A vertical shift refers to the transformation of a graph where the entire graph is moved up or down along the y-axis. This happens when a constant is added or subtracted to the function.
Vertical Shift Definition:
If you have a function f(x), and it is transformed to f(x) + k, where k is a constant, the graph shifts up by k units if k > 0, or down by k units if k < 0.
Example:
If f(x) = x^2, then:
f(x) + 3 = x^2 + 3 shifts the graph up 3 units.
f(x) - 2 = x^2 - 2 shifts the graph down 2 units.
Why does this happen?
The transformation f(x) + k changes the output of the function.
When you add k, every point on the graph is moved up by k units because you are increasing the value of the function at each x-coordinate.
When you subtract k, every point on the graph is moved down by k units because you are decreasing the value of the function at each x-coordinate.
Summary:
A vertical shift occurs when you add or subtract a constant k to the entire function. This shifts the graph up if k > 0 or down if k < 0 without changing the shape of the graph.