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Learning Math Home
Patterns, Functions, and Algebra
 
Session 8 Part A Part B Part C Homework
 
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Session 8, Part C:
Different Functions (35 minutes)

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

 
Linear Function Increasing Exponential Function
 

Exponential Decay Function
y = bx, where b < 1

 

Quadratic Function
y = ax2 + bx + c

 
Exponential Decay Function Quadratic Function
 

Cyclic Function
outputs repeat

 

Inverse Proportion
y = k / x, or xy = k

 
Cyclic Function Inverse Proportion
 

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

show answers
 

 

Problem C2

Solution  

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.

shared points on a function

Which function corresponds to which number?


Take it Further

Problem C3

Solution  

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

Because there is only one line between two points, any different function would have to be nonlinear.   Close Tip


 

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