functions copyright 2014 scott storla. the basic graphs

Functions

Copyright 2014 Scott Storla

What will be the cost of one year of community college in 2016?


Idea

1. Gather data on past costs.

2. Make a picture of the data to look for a pattern.

3. If a pattern exists, describe the pattern using numbers, operations, grouping and variables.

4. Predict the past or future using the result of step 3.

Step 1. Gather data



Step 2. Graph the data


Step 2. Look for patterns


Step 2. Graph the data


Step 2. Look for patterns


Step 3. Model using algebra


Step 4. Predict the futureWhat’s the cost in 2016?

Around $5,800

What’s the cost in 2016?

99 4563y x

99 12 4563y

$5,751y


Written

Graph

Equation Data Table99 4563y x

I’d like to use the year to predict the cost of college.

Domain and Range



0

3

4

8

40

48

50

54

A function in two variables assigns each element from a “domain” set to a specific element in a “range” set.

Domain Range



Domain

Independent variable

Input

Explanatory variable

Manipulated variable

Controlled variable

Range

Dependent variable

Output

Response variable

Response variable

Measured variable


0

3

4

8

40

48

50

54

Year since 2005 Deer in the park


Domain Range


0

3

4

8

40

48

50

54

Year since 2005 Deer in the park

Not a function



0

3

4

8

40

48

50

54

Days without rain Pond level (inches)



99 4563y x

Graph

I’d like to predict the cost of college given the year.

Domain and Range

Domain Range

Domain

Range

DomainRange


99 4563y x


Domain and Range

Domain Range

Domain

Range

DomainRange

Domain and Range


Describing a Data Table Algebraically



99 4563y x

Graph


Describing a data table algebraically


The Basic Graphs

The linear function y x

The quadratic function 2y x

The square root function y x

The exponential function xy e

The logarithmic function lny x


This graph can be approximated using the quadratic function;

20.1 21.5 63.3y x

To predicted the number of subscribers (in millions) in 2001 (the peak year).

Substitute 21 for x and solve for y.

20.1 21.5 63.3y x

20.1 21 21.5 63.3y

63.2y

In 2001 there were about 63.2 million subscribers.


Use the graph to predict the first year there were 50 million subscribers.

This graph can be approximated using the quadratic function;

20.1 21.5 63.3y x

To predict the year the number of subscribers will return to 50 million. Substitute 50 for y and solve for x

Continue the curve and predict when the number of subscribers will return to 50 million.

20.1 21.5 63.3y x

250 0.1 21.5 63.3x

Oper Inv

21.5 21.5

^2

0.1 0.1

63.3 63.3

133 21.5x

21.5 133 x

10 or 33x x

There will be 50 million subscribers in 1990 and again in 2013


b. Replace y with 40 to find the approximate age of a boy (in months) that is 40 cm tall.

This graph can be approximated using the square root function;

2.9 20.1y x

a. Predict the height of a boy that is 35 months old by replacing x with 35.


a. Replace x with 12 to predict the pieces of malware in 2015.

This graph can be approximated using the exponential function;

0.590.82 xy e

b. Replace y with 100 to predict the first year that the number of pieces of malware will reach one hundred million.

Describing a Data Table Algebraically


functions copyright 2014 scott storla. the basic graphs

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