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) = 1/3 |x|
f(x) = 9|x|

Answer 1

C

Explanation:

Answer 2

Answer: f(x) = (1/3)*IxI

Explanation:

Ok, this is a problem of transformations.

First, if we have f(x), then:

f(x - a) is a translation of a units in the x-axis

f(x) + a is a translation of a units in the y-axis.

a*f(x) is a dilation/contraction.

if a is greater than 1, then the graph will be steeper (less wide)

if a is smaller than 1, then the graph will be wider.

Looking at the options, the correct option is:

f(x) = (1/3)*IxI

where we can see that a = (1/3)