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Polynomial, rational, exponential and logarithmic functions and graph

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To exercise your skills, you are to perform the following using different tools available to you (e.g. Excel spreadsheet, graphing calculator, etc.) and write and explanation on your findings:

The graph of: f(x)= 0
The graph of: f(x) = a0 , where a0 ≠ 0
The graph of: f(x) = a0 + a1x , where a1 ≠ 0
For each of the three above:

What does the graph look like- describe the x placement
What is the graph function called?
Give an example of a number you could place in for the variable x, and describe the shift from the original graph. Remember to note what your value you are calculating for the variable x.

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Solution Summary

This solution graphs 3 functions and answers questions pertaining to x placement, calling graph functions and shifts from original graphs.

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The graph of: f(x) = 0
Whatever be the value of x, y will always be 0. So the graph is actually the x axis. This is a constant function. Any change in value of x does not shift the graph, as f(x) is independent of x.

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The graph of: f(x) = a_0 where a_0 ≠ 0
Suppose a_0 = 1 ≠ 0 ...

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