Question

Absolute value and piecewise function explanation tooo plz

Answer 1

Because of the "x-5" in the absolute value, the pieces will separate at x=5, because that's where x-5 = 0.

(This knocks out answer #1, 3, and 4)

To confirm option #2 is correct:

If you pick a number greater than 5, the absolute value doesn't do anything, so

  if x > 5, a(x) = (x-5) + 1

If you pick a number less than 5, "x-5" is negative and the absolute value gives you the opposite of that value:

  if x < 5, a(x) = - (x-5) +1

The answer is the second option.