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Rule

# Horizontal Stretch and Shrink

By multiplying the input of a function by a factor $a > 0,$ its graph can be horizontally stretched or shrunk. $g(x) = f(a \cdot x)$ If $a > 1,$ every input value will be changed as though it was further away from $x = 0$ than it really is. This leads to the graph being shrunk horizontally — every part of the graph is moved closer to the $y$-axis. In the same fashion, $a < 1$ leads to a horizontal stretch. The horizontal distance between the graph and the $y$-axis is changed by a factor of $\frac 1 a.$

Stretch graph horizontally

Note that $y$-intercepts have the $x$-value $0,$ which is why they are not affected by this transformation.