The graph in the question is of the function f(x)=[tex]log _{0.2}x[/tex] which is option a.
Given a graph which is downward sloping and we are required to find the function whose the graph is.
Function is like a relationship between two or more variables expressed in equal to form. It may be a linear function,exponential function, logarithmic function or quadratic function.
In the given graph the values of y becomes negative when the curve crosses then x axis. For all x>1 the value of log x is greater than 0. So the value of [tex]log_{2}x,log_{4}x,log_{20}x[/tex] should be greater than 0 for x greater than 1. But in graph it is negative. That's why the graph will be of y=[tex]log_{0.2}x[/tex].
Hence the given graph is of the function f(x)=[tex]log _{0.2}x[/tex] which is option a.
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