The function h(x) is defined as shown.

what is the range of h(x)?
a) –∞ < f(x) < ∞
b) f(x) ≤ 5
c) f(x) ≥ 5
d) f(x) ≥ 3

h(x)= { x + 2, x < 3
{ -x + 8. x ≥ 3

1. For x<3, h(x)=x+2

now x+2 is an increasing line (a practical way to check, h(1)=3, h(2)=4)

the largest value it takes is at 3, not inclusive, so h(3)=5 not inclusive.

Range_1= (-∞, 5)

2. for x> or equal to 3, h(x)=-x+8, which is a decreasing line (check h(4)=4, h(5)=3 )

so this line takes its maximal value at x=3, f(3)=5 and then takes any other value to -∞.

Range_2=(-∞,5]

3. Range(h)=Range1∪Range2=(-∞, 5)∪(-∞,5]=(-∞,5]      (B)

What’s your question.