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Polynomial, rational, exponential and logarithmic functions and graph

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.

Solution Preview

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.

See attached

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

Solution Summary

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