1.6 common functions and their graphs

(3) Exponentials and Logarithms

It’s important to know what exponential functions are and what their graphs look like.

The exponential functions are the functions like: . And their graphs are like the picture below.

There are a few points we need to know about the graphs of exponentials. Firstly, the domain of the function is the collection of real numbers and the range is all positive real numbers. Secondly, the intercept on the y axis is always 1. Thirdly, the left part of the graph is a horizontal asymptote. The asymptote is the curve that is approaching the x axis little by little but they will never touch the x axis (no matter how close they are), or we may be able to say that they will intersect at negative infinity.

Logarithms look pretty like the exponential function, but it reflects about the ‘mirror’ (a line which formula is y=x). this is the graph of a logarithm function.

The logarithms are functions like: . There are also some points we need to talk about. The domain of the function is (0,+∞). The range is all real numbers and it has a vertical asymptote at the y axis.