Graphing a function... i need to know how to graph two points g(x)=1/2log3(x-4)?

Question

ok so heres the deal.. i need to graph only two points in this fuction and draw the asymptotes (if any)... i have no idea how to do this so a complete explanation would be appreciated... btw the graph i have to do this in cant go any higher that 8 and -8 on the y and x axis

Answer 1

Your points don't look right to me.  They would be correct if the function were

    g(x) = (1/2) log_3(x-4) - 4

...but that's not the function I see listed.  It looks to me as though your function goes through the points (5,0) and (7,.5).

The asymptote for a logarithm is the vertical line corresponding to taking the log of zero.  Notice that when x=4, computing g(x) requires that we find log_3(4-4) = log_3(0), which does not exist.  The vertical asymptote is x=4.