Horizontal 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 horizontal shrink refers to the transformation of a graph where the function is compressed or "squeezed" toward the y-axis. This happens when the input variable x is multiplied by a constant factor greater than 1 inside the function.
Horizontal Shrink Definition:
If you have a function f(x), and it is transformed to f(kx), where k > 1, the graph is compressed horizontally toward the y-axis by a factor of 1/k.
In simpler terms, multiplying the input x by a constant k greater than 1 "shrinks" the graph along the x-axis, making it narrower.
Example:
Let's look at a simple function f(x) = x^2:
The function f(x) = x^2 has a standard U-shaped graph.
If we transform it to f(2x) = (2x)^2, the graph of the function will be compressed horizontally by a factor of 2. This means the graph will look narrower than the original.
Why does this happen?
When you multiply the input by a factor greater than 1, each value of x needs to change faster to reach the same y-value. So, the graph gets "squeezed" toward the y-axis. In other words, for the same y-value, the graph reaches that value with smaller x-values.
For instance:
In f(x) = x^2, to reach y = 4, x needs to be positive or negative 2.
In f(2x) = (2x)^2, to reach y = 4, x only needs to be positive or negative 1. This shows the horizontal compression because the points reach the same y-value faster.
Summary:
A horizontal shrink happens when the function is transformed by multiplying x by a constant k greater than 1 (i.e., f(kx) where k > 1). This causes the graph to get narrower by compressing it along the x-axis.