Question

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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| – 2f(x) = 3|x – 2|f(x) = 3/4 |x – 2|f(x) = 4/3 |x| + 2

Answer 1

Answer:

Required function - $h(x)=|x-2|$  

Step-by-step explanation:

Given : The parent function $f(x)=|x|$  and is translated to the right 2 units.

To find : Which absolute value function has a graph that is wider than the parent function?

Solution :

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 right by 2 unit and form 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 of equal to 1. If k is more than 1 then the graph 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 the attached graph below.

Answer 2

Case 1:  If we multiply f(x) = |x| by a fraction greater than zero and less than 1, the width of the resulting graph will increase.  If the vertex of the original function is moved 2 units to the right, then we'd replace |x| with |x-2|  Only the coefficient (3/4) satisfies the "wider graph" requirement here.

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