Chapter 8 - Section 8.5 - Shifting and Reflecting Graphs of Function - Practice - Page 611: 3

Please see the graph.

Green line: $f(x) = abs (x)$ Red line: $g(x) = abs (x+2)$ We pick three values of $x$ to determine the applicable value of the function (and the y-coordinate). We pick $x=-2$, $x=0$, and $x=2$. $x=-2$ Green line: $f(x) = abs (x)$ $f(x) = abs (x)$ $f(x) = abs (x)$ $f(-2) = abs (-2)$ $f(-2)=2$ $x=0$ Green line: $f(x) = abs (x)$ $f(x) = abs (x)$ $f(x) = abs (x)$ $f(0) = abs (0)$ $f(0)=0$ $x=2$ Green line: $f(x) = abs (x)$ $f(x) = abs (x)$ $f(x) = abs (x)$ $f(2) = abs (2)$ $f(2)=2$ The points $(-2,2)$, $(0,0)$, and $(2,2)$ are on the green line. $x=-2$ Red line: $g(x) = abs (x+2)$ $g(x) = abs (x+2)$ $g(x) = abs (x+2)$ $g(-2) = abs (-2+2)$ $g(-2) = abs (0)$ $g(-2)=0$ $x=0$ Red line: $g(x) = abs (x+2)$ $g(x) = abs (x+2)$ $g(x) = abs (x+2)$ $g(0) = abs (0+2)$ $g(0)=abs 2$ $g(0)=2$ $x=2$ Red line: $g(x) = abs (x+2)$ $g(x) = abs (x+2)$ $g(x) = abs (x+2)$ $g(2) = abs (2+2)$ $g(2) = abs 4$ $g(2)=4$ The points $(-2,4)$, $(0,2)$, and $(2,4)$ are on the green line. However, we are told to not plot points on the graph. The green graph has its vertex at $x=0$, and the red graph is shifted two units to the left. (The red graph has its vertex at $x=-2$.)