Graphs of Logarithmic Functions

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In this lesson, we will look at the graphs of logarithmic functions.

Example:

Given f(x) = log a (x) , a > 0 and a ≠ 1.

a) Find the domain and range of the function f(x)

b) Find the vertical asymptote.

c) Find the x and y intercepts of the graph (if any)

Solution:

a) Since x > 0, the domain is (0, + ∞ ). The range is ( – ∞ , + ∞ )

b) The vertical asymptote is at x = 0

c) The x-intercept is (1, 0) and there is no y-intercept.

Graph of Logarithmic Functions
In science classes we will often find ourselves graphing logarithmic functions to describe situations such as motion or speed over time. When trying to identify these situations as those seen in graphing logarithmic functions, it is important to be able to recognize these graphs. It is also important to recognize graphs of exponential functions and their importance as the logarithmic inverse.
Example:
Graph f(x) = log₂x

• Show Step-by-step Solutions

Graphing Logarithmic Functions
Example:
Graph g(x) = log₃x

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