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 [tex](-\infty,4)[/tex].
Let's try [tex]x=4[/tex] even though we are forbidden to put 4 inside [tex]h[/tex] we are still able to do so.
So [tex]h(4)=0.5\cdot4-1=2-1=1[/tex] what we just got is the upper limit of the range. The lower limit is [tex]h(-\infty)=-\infty[/tex].
So the range is just [tex](-\infty, 1)[/tex].
Hope this helps :)
