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Q:

# How do I graph logarithmic functions?

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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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## Related Questions

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The cosh(x) function is the mathematical hyperbolic cosine function, and it is used to describe the shape of a hanging cable and may sometimes appear as ch(x). The hyperbolic cosine function is a part of the hyperbolic function family which is based on standard trigonometric functions. The cosh(x) function, when combined with the sinh(t) function, describes the right half of a hyperbola.

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A piecewise function is simply two or more functions put together with non-intersecting domains. Once each domain has been determined and the endpoints have been carefully reviewed, then the graph can be completed.

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The domain and range of a function designate the values at which the function exists. In a composite function, one function is being applied to another. You must determine values at which the first function does not exist and values for which the first function creates values where the second function does not exist. This process usually takes only a few minutes to complete.