Q:
# How Do I Graph Logarithmic Functions?

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.

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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.

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