Having identified that, the logarithmic function y = log b x is the inverse function of the exponential function y = b x. We deserve to now proceed to graphing logarithmic features by looking at the relationship in between exponential and logarithmic functions.

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But prior to jumping right into the topic of graphing logarithmic functions, it vital we familiarize ourselves with the complying with terms:

The domain that a function

The domain that a role is a collection of values you deserve to substitute in the role to get an agree answer.

The range of a function

This is the collection of values you acquire after substituting the values in the domain for the variable.


There space three types of asymptotes, namely; vertical, horizontal, and also oblique. The upright asymptote is the worth of x where duty grows there is no bound nearby.

Horizontal asymptotes are constant values that f(x) ideologies as x grows without bound. Slope asymptotes are an initial degree polynomials which f(x) it s okay close as x grow without bound.

How come Graph Logarithmic Functions?

Graphing a logarithmic role can be done by analyzing the exponential function graph and also then swapping x and also y.

The graph of an exponential role f (x) = b x or y = b x consists of the complying with features:

The domain of an exponential duty is actual numbers (-infinity, infinity).The variety is also positive genuine numbers (0, infinity)The graph of one exponential duty normally passes with the allude (0, 1). This means that the y – intercept is at the suggest (0, 1).The graph of one exponential duty f(x) = b x has actually a horizontal asymptote in ~ y = 0.An exponential graph decreases native left to ideal if 0 If the base of the role f(x) = b x is greater than 1, then its graph will boost from left come right and also is referred to as exponential growth.

By looking in ~ the above features one at a time, us can likewise deduce functions of logarithmic attributes as follows:

A logarithmic duty will have actually the domain together (0, infinity).The range of a logarithmic duty is (−infinity, infinity).The logarithmic role graph passes with the suggest (1, 0), i m sorry is the inverse of (0, 1) for an exponential function.The graph of a logarithmic function has a upright asymptote in ~ x = 0.The graph that a logarithmic role will decrease from left to right if 0 and if the basic of the role is better than 1, b > 1, then the graph will increase from left to right.

How to graph a straightforward logarithmic function?

A straightforward logarithmic duty is usually a function with no horizontal or vertical shift.

Here room the steps for developing a graph that a basic logarithmic function.

Since all logarithmic functions pass with the point (1, 0), we locate and also place a dot at the point.To protect against the curve from emotional the y-axis, we draw an asymptote in ~ x = 0.If the base of the duty is higher than 1, increase your curve from left to right. Similarly, if the basic is much less than 1, diminish the curve indigenous left come right.

Now let’s look at the adhering to examples:

Example 1

Graph the logarithmic function f(x) = log in 2 x and state variety and domain that the function.

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Obviously, a logarithmic duty must have the domain and variety of (0, infinity) and also (−infinity, infinity)Since the duty f(x) = log 2 x is greater than 1, we will boost our curve from left to right, a presented below.We can’t see the upright asymptote at x = 0 due to the fact that it’s surprise by the y- axis.