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

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

Reason: Multiplying |x| by a factor a with |a|<1 produces a vertical shrink (less steep), so the V opens wider. The +3 and (x−6) are shifts (no width change), and 9|x| is steeper (narrower).