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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

Respuesta :

frika

Answer:

See explanation

Step-by-step explanation:

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

a) To graph the function [tex]f(x)=|x+2|,[/tex] 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 [tex]g(x),[/tex] translate the graph of the function [tex]f(x)[/tex] 4 units up. The vertex of this graph will be translated vertex of the [tex]f(x)[/tex] graph and will be at point (-2,4) (red line in attached diagram).

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

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