To graph the functions without going through the entire process of transforming the parent function, we can make two tables of values. Then, we only need to plot and connect the obtained points and compare the graphs.
Graph
Let's begin with creating a table of values for f(x).
Note that we can rewrite g(x) in terms of f(x), because g is of the form y=f(ax). Looking at the functions we can see that a= 3.
lf(x)=|x-4| g(x)=| 3x-4| ⇒ g(x)=f( 3x)
The graph of g(x) is a horizontal shrink of the graph of f(x) by a factor of 1 3. The y-intercept is the same for both graphs. When the input value of f(x) is three times the input value of g(x), the output values of f(x) and g(x) are the same.
