Question

graph this function and determine the domain,range and vertical asymptote.

f(x)=In(4-x) no need to graph just assist with points

Answer 1

Here is a nice little page that will give you a quick graph
Just type
log(4-x) into the first window, and click on "Draw"
http://rechneronline.de/function-graphs/

Remember, we can only take log of positive numbers
so 4-x > 0
-x > -4
x < 4
So there is a vertical asymtpote at x = 4
the domain is x < 4
range: y ∊ R

to get the graph, on your calculator find some critical points, e.g.
x = 3.999 -- (3.999 , -6.9)
x = 0 ---- (0, 1.39)
x = 3 --- (3 , 0)
x = -5 --- (-5 , 2.2)
x = -1000 --- (-1000 , 6.9) ---> just to show what happens at the far left.