Question

5. h(x)=0.5x - 1 with domain (-♾, 4) what is the range

Answer 1

We have a domain of a function, that is, which x-es can we throw in. But we are asking which y-s will we get given that we can only throw x-es in $(-\infty,4)$.

Let's try $x=4$ even though we are forbidden to put 4 inside $h$ we are still able to do so.

So $h(4)=0.5\cdot4-1=2-1=1$ what we just got is the upper limit of the range. The lower limit is $h(-\infty)=-\infty$.

So the range is just $(-\infty, 1)$.

Hope this helps :)