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Horizontal Stretch and Shrink

Rule

Horizontal Stretch and Shrink

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

Stretch graph horizontally

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