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Linear and Nonlinear Functions

Linear and Nonlinear Functions. Identifying functions on tables, graphs, and equations. Irma Crespo 2010. 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. Yards to Feet.

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Linear and Nonlinear Functions

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  1. Linear and Nonlinear Functions Identifying functions on tables, graphs, and equations. Irma Crespo 2010

  2. 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.

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

  4. linear nonlinear Tables: Linear or Nonlinear • Is the rate of change constant (the same)? +3 +15 +2 -15 +2 -15 +3 +33 +2 +3 +51 -15

  5. Identify: Linear or Nonlinear Table? • linear • nonlinear

  6. Graphs: Linear or Nonlinear • Is the graph a straight line? • linear • nonlinear • linear

  7. Identify: Linear or Nonlinear Graph? • linear • linear • nonlinear

  8. 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

  9. y = + 1 3x 2 Identify:Linear or Nonlinear Equation? y = .6x1 y = x2 + 8 y = 2/x + 5 linear nonlinear linear nonlinear

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

  11. y = + 5 8 x a b c Exit Slip • Identify if linear or nonlinear. Table A Equation Graph

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

  13. 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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