How do you find a range of h(x)?
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The range of h(x) are all the outputs
x+2 x< 3
-x +8 x ≥ 3
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Range 1
x= 3
h(x) = x+2
h(x) = 3+2=5 (h(3)=5 not inclusive)
h(x) = 5
Range 1 = (-∞, 5)
Range 2
x= 3
h(x) = -x +8
h(x) = -3 +8
h(x) = 5
h(x) = 5 ( It is a decreasing line, so 5 is the maximum value)
Range 2 = (-∞,5]
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Range (h) = (-∞, 5) U (-∞,5] = (-∞,5]
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Answer
Range = (-∞,5]
Range ≤ 5