By multiplying the input of a function by a factor a>0, its graph can be horizontally stretched or shrunk.
g(x)=f(a⋅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 a1.
y-intercepts have the x-value 0, which is why they are not affected by this transformation.
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