Final answer:
Graphing a logarithmic function involves identifying key points, determining the vertical asymptote, plotting the curve smoothly, and specifying the domain (all positive real numbers) and range (all real numbers). For wide-ranging values, using a logarithmic scale can be helpful. The correct option is a.
Step-by-step explanation:
To graph a logarithmic function, you will need to identify a few components. First, decide on key points by selecting values for the independent variable and calculating the corresponding logarithmic values for the dependent variable. Next, determine the asymptote, which for standard logarithmic functions is the y-axis (x=0) where the function approaches but never touches. When plotting the curve, be sure to use a smooth, continuous line illustrating the exponential growth or decay, depending on the base of the logarithm.
The domain of a basic logarithmic function is all positive real numbers, since you cannot take the logarithm of zero or negative numbers. The range, however, is all real numbers, since the output of a logarithmic function can be any real number. To properly scale your graph, especially if the values cover a wide range, consider using a logarithmic scale for the axes.