Question

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

Answer 1

f(x)=9|x|
.................

Answer 2

Answer:

The correct option is 3.

Step-by-step 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

$f(x)=\frac{1}{3}|x|$

In this function $a=\frac{1}{3}<1$. 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.