Question

how do you graph logarithmic functions?

Answer 1

We first start with the properties of the graph of the basic logarithmic function of base a,

f (x) = log a (x) , a > 0 and a not equal to 1.

The domain of function f is the interval (0 , +inf). The range of f is the interval (-inf , +inf).

The symbol 'inf' means infinity.

Function f has a vertical asymptote given by x = 0. This function has an x intercept at (1 , 0). f increases as x increases.

Answer 2

The logarithmic function will be a reflection of the function y=10^x over the line y=x. We know that the logarithmic function f(x)=logx is undefined for an negative value because no exponent will ever give you a negative value. So the graph approaches the y-axis asymptotically. It is increasing from left to right with an x-intercept at x=1 because the exponent to which you raise 10 to get 1 is 0.