Linear, Quadratic, Exponential, and Absolute Value Functions
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1 Linear, Quadratic, Exponential, and Absolute Value Functions Linear Quadratic Exponential Absolute Value Y = mx + b y = ax 2 + bx + c y = a b x y = x 1
2 What type of graph am I? 2
3 What can you tell me about each type of graph? Linear Exponential Quadratic 3
4 Topic 3: Classify Equations I Can: Classify equations as linear, exponential, quadratic, absolute value or none of these. What have we already learned about linear equations? How many different types of linear equations can you write? 4
5 LINEAR QUADRATIC EXPONENTIAL ABS VALUE 4x + 3y = 24 y 4 = 2(x + 1) 2 y= 20(3.02 x ) 5 3 x = 25 2x = 10 y = 2(x + 1) 3 f(x) = 4x + 3 y = x f(x) = x 2 5 5
6 6
7 How can we distinguish each type of equation? LINEAR QUADRATIC EXPONENTIAL ABS VALUE 7
8 8
9 Linear, Quadratic & Exponential Functions What type of function? (move this box) 9
10 Linear, Quadratic & Exponential Functions What type of function? (move this box) 10
11 Linear, Quadratic & Exponential Functions What type of function? (move this box) 11
12 Linear, Quadratic & Exponential Functions In the real world, people often gather data and then must decide what kind of relationship (if any) they think best describes their data. You may be able to use the graph of data points to determine a model for the data. 12
13 Graphing Data to Choose a Model 1 Graph each data set. Which kind of model best 2 describes the data? 3 The data appear to be exponential Plot the data points and connect them. 13
14 Graphing Data to Choose a Model 2 Graph each data set. Which kind of model best describes the data? 2 3 The data appear to be linear Plot the data points and connect them. 14
15 Graphing Data to Choose a Model 3 Graph each data set. Which kind of model best describes the data? 2 3 The data appear to be exponential Plot the data points and connect them. 15
16 Graphing Data to Choose a Model 4 Graph each data set. Which kind of model best describes the data? 2 3 The data appear to be quadratic Plot the data points and connect them. 16
17 Choose a Model from Table Another way to decide which kind of relationship (if any) best describes a data set is to use patterns. We can use what we know about arithmetic sequences (common difference) and geometric sequences (common ratio) to find a pattern and write an equation to model the data. 17
18 Topic 1: Classify Tables I Can: Classify a consistent table as a quadratic, exponential, absolute value, or other function. I can also identify the rate of change. first differences that have a constant ratio. 18
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21 For every constant change of +1 there is a constant rate of change for the Second Difference. Quadratics have constant SECOND DIFFERENCE. 21
22 Determine the type of function: If the pattern continues, when would the oven be 75 0? 22
23 Classify the function from the table: x y What is the y-value when x = 8? 23
24 Classify the function from the table: x y What is the y-value when x = -1? 24
25 Classify the function from the table: x y What is the y-value when x = -2? 25
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27 Attachments ComparingLinear&ExponentialFunctionsTeacher.pdf ComparingLinear&ExponentialFunctionsStudent.doc ComparingLinear&ExponentialFunctionsStudent.pdf Comparing_Linear_and_Exponential_Functions.tns Activity Day 4 TypesFunctionExploration linear and quadratic from I drive.doc Activity Day 4 TypesFunctionExploration cubic and absolute value from I drive.doc graphingfunctions.tns graphingfunctionsteacherguide.doc graphingfunctionsteacherguide.pdf
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