Given `y=log(4-x)`, find the domain, the vertical asymptote and draw the graph.
Consider the function `y=logx` . This function is undefined for `x<=0` , has a vertical asymptote at x=0, and increases on its domain.
The given function reflects the basic log function across the y-axis. Then the given function takes the transformed function and translates it horizontally 4 units to the right. (Or you can translate the log function 4 units left, and then reflect across the y-axis).
(1) The domain is `x<4` since the function is undefined for `x>=4` as the domain of the log function is positive. `4-x` is positive if `x<4`
(2) There is a vertical asymptote at x=4.
The graph of `y=logx` is in black; the graph of `y=log(-x)` is in red (the reflection over the y-axis); and the graph of `y=log(4-x)` is in blue.