Exercise 17 Page 160

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

Graphing y(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 y(x). Note that y(x) is a transformation of the graph of the parent function y=|x|, which is V-shaped. Therefore, y(x) will also be a V-shaped graph.

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

Comparing the Functions

To compare our graph to the graph of f(x)=|x+3|-2, let's first draw this function. We will start with making a table of values just like with function y(x).

Let's use the obtained ordered pairs to graph this function.

Now when we have drawn the graph of f(x), we can compare it to the graph of y(x) by plotting them both on the same coordinate plane.

As we can see, the graph of y(x) is a horizontal translation 1 unit left of the graph f(x).