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In this video tutorial, we focus on graphing logarithmic functions with transformations and how to determine the domain and range. We start with an example equation y = log base 2 of x. The process involves setting the inside equal to zero, one, and the base (in this case, two) to create a table. Setting it equal to zero gives the vertical asymptote, while setting it to one and the base gives points to plot. For example, log base 2 of 1 equals 0, and log base 2 of 2 cancels out.