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{{ printedBook.courseTrack.name }} {{ printedBook.name }} The graph of $y=f(ax)$ is a horizontal stretch or shrink by a factor of $a1 $ of the graph of $y=f(x)$ as long as two conditions are met. $a>0anda =1$ A horizontal stretch means the new function is going further away from the $y$-axis and a horizontal shrink means it comes closer to the $y$-axis. Whether the transformation is a stretch or shrink depends on the value of $a.$ $Horizontal shrink:Horizontal stretch: a>10<a<1 $ Let's look in the diagram and mark corresponding points in the graphs.

From the graph, we see that the function $g(x)=f(2x)$ is coming closer to the $y$-axis. In other words, the graph of $g(x)$ is a horizontal shrink of the graph of $f(x)$ by a factor of $21 .$