Vertical Stretch
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 stretch refers to the transformation of a graph where the graph is "stretched" or "pulled" vertically away from the x-axis. This occurs when the function is multiplied by a constant factor greater than 1.
Vertical Stretch Definition:
If you have a function f(x), and it is transformed to c • f(x), where c > 1, the graph undergoes a vertical stretch by a factor of c.
In simpler terms, multiplying the function by a constant c greater than 1 causes the graph to become "taller" or "stretched" vertically, making it farther away from the x-axis.
Example:
Let’s consider the function f(x) = x^2:
The function f(x) = x^2 has a standard U-shaped graph.
If we transform it to 2 • f(x) = 2 • x^2, the graph is vertically stretched by a factor of 2. This means the graph becomes taller and farther from the x-axis.
Why does this happen?
When you multiply the function by a constant greater than 1, the output values increase.
For each x-value, the y-value (the output) becomes larger than it was in the original function. This stretching makes the graph "taller" or "steeper" vertically.
For example:
In f(x) = x^2, at x = 2, the output is f(2) = 4.
In 2 • f(x) = 2 • x^2, at x = 2, the output is f(2) = 8, which is double the original value.
Summary:
A vertical stretch happens when the function is transformed by multiplying it by a constant c where c > 1. This causes the graph to become taller or "stretched" vertically, making it farther away from the x-axis.