Test IV.
3.
𝑓(𝑥) = |𝑥 + 3| − |𝑥 − 4|
a. (−∞, −3)
−∞ < 𝑥 < −3, 𝑥 + 3 < 0 and 𝑥 − 4 < 0
𝑓(𝑥) = −(𝑥 + 3) + (𝑥 − 4)
𝑓(𝑥) = −7
b. [−3, 4)
−3 ≤ 𝑥 < 4, 𝑥 + 3 > 0 and 𝑥 − 4 < 0
𝑓(𝑥) = (𝑥 + 3) + (𝑥 − 4)
𝑓(𝑥) = 2𝑥 − 1
c. [4, ∞)
4 ≤ 𝑥 < ∞, 𝑥 + 3 > 0 and 𝑥 − 4 > 0
𝑓(𝑥) = (𝑥 + 3) − (𝑥 − 4)
𝑓(𝑥) = 7