Answer: 11
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Explanation:
This is a piecewise function. The h(x) piecewise function has two identities and it depends on what the x input is.
- If x = -4 or smaller, then h(x) = -0.5x-15
- If x > -4, then h(x) = 20 - 3x^2
We can only pick one piece at a time.
To compute h(-4), we'll use the first rule shown above since the input is x = -4
So,
h(x) = -0.5x - 15
h(-4) = -0.5(-4) - 15
h(-4) = 2 - 15
h(-4) = -13
To compute h(-2), we'll use the second rule since the input x = -2 is larger than -4. In other words, x = -2 makes x > -4 true.
h(x) = 20 - 3x^2
h(-2) = 20 - 3(-2)^2
h(-2) = 20 - 3(4)
h(-2) = 20 - 12
h(-2) = 8
Therefore,
h(-4) + 3h(-2) = -13 + 3(8) = -13 + 24 = 11
