What is the relationship of the graph of an exponential function and its inverse?

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

1) What is the relationship of the graph of an exponential function and its inverse? Graph of Exponential Function vs Graph of Inverse of Exponential Function

2) How can you use the properties of exponents to represent an exponential function as a logarithm?

3) How are logarithms used to solve exponential functions?

4) Give a real world example of where set theory/set notation would be used.  Explain why it would be necessary and how it can be applied.

5) Explain why the functions y = 3 -x  and y = (1/3)x  create the exact same graph.  Be thorough in your explanation.

6) If you graph the function y = 3x  and y = 3 –x  the graphs create a reflection about the y-axis.  Explain why this occurs.

7) Now, if you graph the function y = 3x  and y = -(3x)  the graphs create a reflection about the x-axis instead.  Explain why, in detail,  the reflection  changes from being about the y-axis to being about the x-axis.

8) Now, know the answers to #11 and #12, if we take the base function y = 3x what would cause a reflection about the origin?  Explain why this happens.

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