Outcome: C29

 

                   Analyse tables and graphs to distinguish between linear, quadratic, and exponential functions

 

Originator: Stefan and Ashlie

 

Explanation:

A function represents the dependence of two different units. Where there is one input value (usually x) and one result (usually y). A functuion gives for every input value only one result. So every x value represents only one y value. Functions also can be represented graphically.

To differentiate between linear, quadratic, and exponential functions it first depends on if you are having a graph or a table.

 

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Graphs

 

Linear Function(Arithmetic)	Quadratic Function	Exponential Function

A linear function is always a straight line, a quadratic funtion a V shaped curve and an exponential one just a curve.

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Tabels

 To determine what kind of funtion you have in the table in front of you, you should do some calculations first.

 A linear function has a common difference, means in/decreases every step by the same amount. A quadratic funtion has the same common difference on the secon degree. If you think you have a exponential function in front of yourself then tn/t(n-1)=t(n+1)/(t(

 

 

y value	1	2	3	4	5	6
x value	-5	1	7	13	19	25

This table represents a linear function because it increses by every x value by the certain amount of 6(common difference)

The equation for this tabe is y=6x+(-11)

 

 

y value	1	2	3	4	5	6
x value	3	6	11	18	27	38

This table represnts a Quadratic equation because its common ratio is in the second degree.

D1 = {3, 5, 7, 9, 11, ...}

D2 = {2, 2, 2, 2, ...}

The equation for this table is y=x^2+2

 

 

y value	1	2	3	4	5	6
x value	6	24	96	384	1536	6144

This table represents a Exponential function because the common difference is 4

The equation for this table is y=6*4^(x-1)

 

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Sample Problems

 

Distinguish if the following tables/graphs are linear, quadratic or exponential functions. 

y value	1	2	3	4	5	6
x value	-1	3	7	11	15	19

This table ishows a common difference.

Because of that it represents a linear function.

The Equation of the table is y=4x+(-5)

 

 

This graph represents a straight line.

Because of that the graph represents a linear function

 

 

Source: all pictures created with http://www.e-tutor.com/et2/graphing