## Drawing log graphs

First lets consider the basic log graph

The important features

- The graph has an asymptote of
- It intersects the x axis at , because the log of 1 is zero
- It passes through the point , because . Notice 10 is the base
- The curve is always increasing, but at a slower and slower rate

Conclusions

The asymptote will always be unless the graph is translated has an asymptote at

when equals the base number unless the graph has been translated goes through

The graph goes through (1,0) unless translated goes through the point

Examples

For each of the function below give the asymptote, the coordinates where the point has moved to and the coordinates of where the point has moved to.

The asymptote has not changed since we have not added to so the asymptote is

The point related to the base is

The point has not moved since we have not added to or

The asymptote has not changed since we have not added to so the asymptote is .

The point related to the base is because we have added 2 to the function so the graph have moved up 2.

The point has moved to since we have added 2 to the function so the graph have moved up 2.

The asymptote is because we have subtracted 1 from x and this shifts the graph 1 place to the right.

The point related to the base is because the y values are 3 times bigger and then we add 2.

The point has moved to since we need to multiply y by 3 (no effect here) and then add 2.