Exercise 16 Page 160

Let's graph $g(x)$ first and then we can compare it to the graph of $f(x).$

Graphing $g(x)$

To graph the function without going through the entire process of transforming the parent function, we can make a table of values. Then we only need to plot the ordered pairs that we find.

Now we can plot these ordered pairs on a coordinate plane and connect them to get the graph of $g(x).$ Note that $g(x)$ is a transformation of the graph of the parent function $y=|x|,$ which is V-shaped. Therefore, $g(x)$ will also be a V-shaped graph.

Now that we have graphed our function, we can move on to comparing it to $f(x).$

Comparing the Functions

To compare our graph to the graph of $f(x)=|x-6|,$ let's first draw this $f(x).$ Note that this function is a horizontal translation $6$ units right of the graph $y=|x|.$

Now when we have drawn function $f(x),$ we can compare $g(x)$ to it by drawing them on the same coordinate plane.

As we can see, the graph of $g(x)$ is a horizontal translation $5$ units left of the graph $f(x).$