We've seen many different kinds of functions in the past few sessions. We've examined characteristics of functions, looked at their graphs, and explored situations where they arise. In general, people tend to think in terms of linear functions, trying to fit given data into lines. What we've seen, however, is that there are many other kinds of functions. Here are examples of their equations and graphs:
Note 8

Linear Function y = ax + b		Exponential Growth Function y = bx, where b > 1

Exponential Decay Function y = bx, where b < 1		Quadratic Function y = ax2 + bx + c

Cyclic Function outputs repeat		Inverse Proportion y = k / x, or xy = k

It's important to be familiar with various kinds of functions. Many different functions might fit just a few pieces of data. Here's an example to show how this might happen.

Problem C1

Fill in the missing entries according to the rules given above.

Input Linear function 2*(input) Quadratic function (input)2 - (input) + 2 Exponential function 2(input) 1 2 2 2 2 4 4 4 3 4 5 6 7

hide answers

Problem C2

Here's a picture of the three functions given above, showing how they share the same two points. A cyclic function also shares those two points.

Which function corresponds to which number?

Problem C3

How many different functions could fit these two data points, (1,2) and (2,4)? Explain your answer. Can you describe one other function that fits these two data points, either with an equation or through some other way? Note 9

Learning Math Home | Algebra Home | Glossary | Map | ©

Session 8: Index | Notes | Solutions | Video