Question

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

a. Graph the follow absolute value function and show your work to determine the vertex:
f(x) =|x + 2|
b. The function g(x) translates f(x) 4 units up. Graph g(x) on the same coordinate plane and write the g(x) function.
c. The function h(x) reflects f(x) over the x-axis. Graph h(x) on the same coordinate plane and write the h(x) function

Answer 1

See explanation

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).