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

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gsenviro | College Teacher | (Level 1) Educator Emeritus

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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.

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