Question

Which absolute value functions will be narrower than the parent function, f(x) = |x|? Check all that apply. f(x) = |x| f(x) = |x – 2| f(x) = |x| + 3 f(x) = 2.9|x| f(x) = 1.2|x + 8| f(x) = 0.7|x| – 3.2

Answer 1

The answer is f(x) = 2.9|x| and f(x) = 1.2|x + 8|

Answer 2

Given parent function is f(x)=|x|

Now we have to find which function from given choices will be narrower than the parent function.

Notice that adding or subtracting some number from the parenth function only shifts the graph up, down, left of right side.

But that will not make function narrorwer or broader.

So f(x) = |x – 2| and  f(x) = |x| + 3, can't be the answer.

Multiplying by some positive real number which is more than 1, makes function narrower.

Only f(x) = 2.9|x| from remaining choices fits that case.

Hence f(x) = 2.9|x| is the final answer.

f(x) = 1.2|x + 8|  will also make the function narrower but will shift the parent function too.