# Graphing and Logarithm help. Graphing domain and range using interval notation

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Expert Answers

gsenviro | Certified Educator

Given function: `g(x) = log_4(x-3)`

The **domain** of a function is defined as all the values of x for which the function exists or is defined. Recall that logarithmic functions are not defined for zero or negative numbers,

i.e., x-3> 0

or, x >3

therefore, the domain of the given function is (3,+`oo`]

The **range** of a function is defined as all the values of g(x) (in this case) for which some x exists such that the function will be defined.

The range of a logarithmic function is the set of real numbers or, g(x) `inRR`

You can use spreadsheet software for plotting the graph. I used Desmos calculator (https://www.desmos.com/calculator) and obtained the graph. Feel free to use any other utility as well.

Hope this helps.