Question

3. Work on the following coordinate plan to graph the following functions:

Answer 1

Answer:

See explanation

Step-by-step explanation:

First, graph the parent function $a(x)=|x|.$ The graph of this function has its vertex at the origin (green graph in attached diagram).

a) To graph the function $f(x)=|x+2|,$ translate the parent graph 2 units to the left. The vertex of this graph will be translated vertex of the parent graph and will be at point (-2,0) (blue line in attached diagram).

b) To graph the function $g(x),$ translate the graph of the function $f(x)$ 4 units up. The vertex of this graph will be translated vertex of the $f(x)$ graph and will be at point (-2,4) (red line in attached diagram).

c) To graph the function $h(x),$ reflect the graph of the function $f(x)$ across the x-axis. The vertex of this graph will the same as the vertex of the $f(x)$ graph (orange line in attached diagram).