Vertical Shrink
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 shrink refers to the transformation of a graph where the graph is compressed or "squeezed" vertically toward the x-axis. This happens when the function is multiplied by a constant factor between 0 and 1.
Vertical Shrink Definition:
If you have a function f(x), and it is transformed to c • f(x), where 0 < c < 1, the graph undergoes a vertical shrink by a factor of c.
In simpler terms, multiplying the function by a constant c between 0 and 1 causes the graph to become "shorter" or "compressed" vertically, making it closer to 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 0.5 • f(x) = 0.5 • x^2, the graph is vertically compressed by a factor of 0.5. This means the graph becomes shorter and closer to the x-axis.
Why does this happen?
When you multiply the function by a constant less than 1, the output values are scaled down.
For each x-value, the y-value (the output) is now smaller than it was in the original function. This compression makes the graph "flatter" or "shorter" vertically.
For example:
In f(x) = x^2, at x = 2, the output is f(2) = 4.
In 0.5 • f(x) = 0.5 • x^2, at x = 2, the output is f(2) = 2, which is half of the original value.
Summary:
A vertical shrink happens when the function is transformed by multiplying it by a constant c where 0<c<1. This causes the graph to become shorter, or "compressed," vertically toward the x-axis.