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**Linear and Nonlinear Functions**

Identifying functions on tables, graphs, and equations. Irma Crespo 2010

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**Warm Up What is the linear equation for this graph? Graph y = 2x + 1**

Rewrite the linear equation 3y + x = 9 to its slope-intercept form or the “y = ” form.

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**Length of a Side of a Square Yard**

Compare and Contrast Yards to Feet Number of Feet Number of Yards Yards to Square Yards Length of a Side of a Square Yard Area of Square (yd2)

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**Tables: Linear or Nonlinear**

Is the rate of change constant (the same)? x y 2 50 4 35 6 20 8 5 x y 1 4 16 7 49 10 100 +3 +15 +2 -15 +2 -15 +3 +33 +2 +3 +51 -15 linear nonlinear

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**Identify: Linear or Nonlinear Table?**

x y 20 5 16 10 12 15 8 x 2 4 6 y 8 18 nonlinear linear

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**Graphs: Linear or Nonlinear**

Is the graph a straight line? linear nonlinear linear

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**Identify: Linear or Nonlinear Graph?**

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**Equations: Linear or Nonlinear**

REMEMBER: x1 = x and x0 = 1 In “y = ” form, is x raised to a power of 1 or 0? Does x appear in the numerator? y = 6/x y = x3 + 1 y = x + 4 nonlinear y = ½ x nonlinear y = 4 linear linear linear

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**Identify:Linear or Nonlinear Equation?**

3x 2 y = .6x1 y = x2 + 8 y = 2/x + 5 linear nonlinear linear nonlinear

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**Pointers to Keep in Mind**

A table is linear if the rate of change is constant. There is a common difference. A graph is linear if it is a straight line. An equation is linear if the power of x is either 1 or 0 and it appears in the numerator.

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**Exit Slip Identify if linear or nonlinear. Table A Equation y = + 5**

3 6 9 12 y 10 8 y = 8 x Graph a b c

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**Practice Worksheet Complete the practice worksheet.**

Work with a partner or on your own. Submit completed worksheet for grading. Solutions are discussed the next day.

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Main Resources Day, et.al. (2009). Math Connects: Concepts, Skills, and Problem Solving. Chapter 10. Columbus:McGraw-Hill. PowerPoint created by Irma Crespo. University of Michigan-Dearborn, School of Education. Winter 2010.

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Comparing Functions and Identifying Linear and Non-linear Functions

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