Question

Use complete sentences to analyze the graph of the function f(x) = log 1/4 x.

Part 1: Describe the domain, range, and general shape of this graph. (4 points)

Part 2: Using complete sentences, explain how plotting specific points helps graph the function and note any critical points such as its intercepts. (4 points)

Answer 1

Logarithmic graphs are almost similar to square root graphs, and they are the inverse of exponential graphs. In order to graph this "by hand", you need to remember that logs are not defined for negative x or for x = 0. Because of this restriction on the domain (the input values) of the log, it isn't even needed to try to find y-values for, say, x = –3 or x = 0. Instead, start with x = 1, and work from there, using the definition of the log. Since log graphs start at (1,0) and square root graphs start at (0,0).

Knowing the critical points of the function would help one form the shape of the graph in order to see if it really is a log graph and/or to find any x or y values of the function.