Question

Which absolute value function has a graph that is wider than the parent function, f(x) = |x|, and is translated to the right 2 units?
f(x) = 1.3|x| – 2
f(x) = 3|x – 2|
f(x) = |x – 2|
f(x) = |x| + 2

Answer 1

The required function -   $h(x)=|x-2|$

The parent function $f(x)=|x|$  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 $f(x)=|x|$

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).

$h(x)=|x-2|$

 If the graph is wider than the parent function then the function must be in the form of,  

$h(x)=K\times f(x)$

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,  $h(x)=|x-2|$  

We plot the graph of both the equations in which translation is shown.

Refer to the attached graph below.

To learn more about the function visit:

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