Question

Consider the function h(x)=12x−3 with a restricted domain of {−2, 0, 2, 10}.What is the range of the function?

Answer 1

3rd option: {-4, -3, -2, 2}

Explanation:

We have the following function:

`h(x)=(1)/(2)x-3`

And it only has as domain: {−2, 0, 2, 10}

So we evaluate at each value and the range would be the corresponding output value for each domain value, just like this:

`\begin{gathered} h(-2)=(1)/(2)\cdot-2-3=-1-3=-4 \\ \\ h(0)=(1)/(2)\cdot0-3=-3 \\ \\ h(2)=(1)/(2)\cdot2-3=1-3=-2 \\ \\ h(10)=(1)/(2)\cdot10-3=5-3=2 \\ \\ \text{ Therefore, the range is:} \\ \\ R={}{}{}\lbrace-4,-3,-2,2\rbrace \end{gathered}`

So the correct answer is 3rd option {-4, -3, -2, 2}