By multiplying the input of a function by a factor $a>0,$ its graph can be horizontally stretched or shrunk. 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 $\frac{1}{a}.$ $y$-intercepts have the $x$-value $0,$ which is why they are not affected by this transformation.