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The graphs of $f(x)=|x|$ and $g(x)=a|x|$ both have vertices located at the origin, so we know that there haven't been any translations. However, $g(x)$ is somewhat shrunk. This means $a$ is less than $1.$ $\begin{gathered} a < 1 \end{gathered}$ To get from the graph of $f(x)$ to the graph of $g(x),$ we need to shrink $f$ away from the $y$-axis. Let's look at a point on each graph with the same $y$-values and compare their $x$-values.
As we can see from the graph, when the $x$-value of $g(x)$ is three times the $x$-value of $f(x),$ the $y$-value is the same for both functions. Therefore, to get $g(x),$ $f(x)$ must be vertically shrunk by a factor of $a=\frac{1}{3}.$