# 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.

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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Q&A Related to "How do I graph logarithmic functions?"
 1. Open the graphing calculator's function graphing menu. On most devices, you do this by hitting the "Y= button. 2. Enter the equation using the buttons for numbers, brackets, http://www.ehow.com/how_8143033_graph-logarithmic-...
 The graph of y = log(x) is defined only for x>0. The graph is a monotonic increasing function over its domain. It starts from an asymptotic "minus infinity" when x approaches http://wiki.answers.com/Q/What_is_the_graph_of_log...
 the one is separated from the log. so it's log base 2 x +1=y . so to find any points, plug in x values, in which you then get your y values. but make sure you add the "one" http://answers.yahoo.com/question/index?qid=201102...
 There are many ways to graph functions. It realy depend on what kind of function you are wanting to graph. There are many of resources out there that can help with the graphing function http://www.ask.com/web-answers/Science/Mathematics...