Question

What is the value of h(a) when a = 2 in the

piecewise function
3a + 2
4a +5
3
h(a) =
when a > 3
when a = 3
when a <3

Answer 1

Answer: 3

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Step-by-step explanation:

This is the given piecewise function

`h(a) = \begin{cases}3a+2 \text{ when } a > 3\\4a+5 \text{ when } a = 3\\3 \text{ when } a < 3\\\end{cases}`

We can rewrite things like this

`\text{when } a > 3, \ \ h(a) = 3a+2\\\text{when } a = 3, \ \ h(a) = 4a+5\\\text{when }a < 3, \ \ h(a) = 3\\`

I personally prefer this format better because it mentions the inputs first, and that leads to which function definition we go for.

The input a = 2 fits the description of
`a < 3` since
`2 < 3` is a true statement. Therefore we go for the third line and can see that
`h(a) = 3` becomes
`h(2) = 3`

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As another example, if we had the input a = 7, then we'd go for the first line (since 7 > 3) and get

h(a) = 3a+2

h(7) = 3(7)+2

h(7) = 23