To graph a logarithmic function, the domain of the function is determined, which is a set of all allowable x values. The domain is used to calculate a range of y values. The vertical asymptote gives the value near which the function changes rapidly. The x and y intercepts are calculated. Using all this information, the graph can be sketched with the coordinates obtained from the domain and range.
For the simplest logarithmic functions, the logs are not defined when x=0 or x is negative. So the domain for such a log equation is restricted to only positive values for x. An equation such as y=log(x+3) would be defined for x values that are greater than -3. Once the domain is determined, y values can be calculated using the x values to determine the range of the function. The asymptote is calculated to determine the values where the y values change exponentially for small increases in x. For y=log x, the asymptote is the line x=0. Therefore, additional values of x should be used between 0 and 1 to calculate y values in order to obtain the coordinates to draw the curve. For y=log(x+3), the asymptote is at x=-3. Therefore the addition x values should fall between x=-2 and x=-3. The x and y intercept are calculated, if applicable for the equation. Once all the (x,y) coordinates are obtained and plotted, the graph can be sketched.