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

None of them. A graph of y = a|x| is wider than y = |x| only when 0 < |a| < 1 (vertical compression). The given functions have a = 1 (|x|, |x|+3, |x−6|) or a = 9 (9|x|), so none produce a wider graph. For example, (1/2)|x| would be wider.