The required function - [tex]h(x)=|x-2|[/tex]
The parent function [tex]f(x)=|x|[/tex] is translated to the right 2 units.
We have to find which absolute value function has a graph that is wider than the parent function.
The parent function [tex]f(x)=|x|[/tex]
with the vertex (0,0)
The parent function is translated to the right 2 units.
Transformation to the right,
f(x)→f(x-b) , the graph of f(x) is shifted towards right by b unit.
Same as the graph f(x) is shifted towards the right by 2 units and forms a graph of h(x).
[tex]h(x)=|x-2|[/tex]
If the graph is wider than the parent function then the function must be in the form of,
[tex]h(x)=K\times f(x)[/tex]
Where the value of k must be less than or equal to 1. If k is more than 1 then the graph is compressed.
So, let it be k=1
Therefore, The required absolute value function is, [tex]h(x)=|x-2|[/tex]
We plot the graph of both the equations in which translation is shown.
Refer to the attached graph below.
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