Question

which absolute value function when graphed will be wider than the graph of the parent function f(x)=|x|

Answer 1

The correct option is 3.

Explanation:

The parent absolute function is

`f(x)=|x|`

The vertex form of an absolute function is

`g(x)=a|x-k|+k`

Where, (h,k) is vertex and a is a constant.

If a>1, then the graph of f(x) stretch vertically by factor a and if 0<a<1, the the graph compressed vertically by factor a.

In option 1, the given function is

`f(x)=|x|+3`

The graph of parent function shifts 3 units up but the size and shape remains same. Therefore option 1 is incorrect.

In option 2, the given function is

`f(x)=|x-6|`

The graph of parent function shifts 6 units right but the size and shape remains same. Therefore option 2 is incorrect.

In option 3, the given function is

`f(x)=(1)/(3)|x|`

In this function
`a=(1)/(3)<1`. It means the graph of parent function compressed vertically by factor 1/3. So, the graph of this function is wider than the graph of the parent function.

Therefore the correct option is 3.

In option 4, the given function is

`f(x)=9|x|`

In this function
`a=9>1`. It means the graph of parent function stretched vertically by factor 9. So, the graph of this function is thinner than the graph of the parent function.

Therefore option 4 is incorrect.