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

ANSWER:

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

STEP-BY-STEP EXPLANATION:

We have the following function:

$h(x)=\frac{1}{2}x-3$

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:

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

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