Question

Which absolute value function, when graphed, will be wider than the graph of the parent function, f(x) = |x|? f(x) = |x| + 3 f(x) = |x − 6| f(x) = |x| f(x) = 9|x|

Answer 1

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Answer 2

Answer:

All the options are incorrect.

Step-by-step explanation:

The parent absolute function is,

$f(x)=|x|$

An absolute function can be in the form of

$f(x)=a|x+b|+c$

Where a>1 shows vertical stretch and a<1 shows vertical compression. b>0 represents horizontal shift towards left and b<0 represents horizontal shift towards right. c>0 represent vertical shift in upward direction and c<0 represent vertical shift in downward direction.

The function in option 1 is,

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

It shows the vertical shift in upward direction by 3 units. Therefore option 1 is incorrect.

The function in option 2 is,

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

It shows the horizontal shift in right direction by 6 units. Therefore option 2 is incorrect.

The function in option 3 is,

$f(x)=|x|$

It is same as the parent function f(x). Therefore option 3 is incorrect.

The function in option 3 is,

$f(x)=9|x|$

It shows the vertical stretch therefore it will not wider than absolute parent function. Option 4 is incorrect.

The graph of f(x) is wider than the parent function if the function is in the form of

$f(x)=a|x|$

Where the value of a is lies between 1 to 1.

So option 3 is correct if the scale factor between 1 to 1 is omitted, otherwise all option are incorrect.