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Linear and Nonlinear Functions Identifying functions on tables, graphs, and equations. Warm Up 1. What is the slope and y-intercept of: 2. Rewrite the linear equation 3y + x = 9 to its slopeintercept form. 3. What is the linear equation for this graph? Linear Functions Linear Functions have graphs that are straight lines and represent constant rate of change. NonLinear Functions Nonlinear Functions have graphs that are not straight lines. The rate of change is not constant (values don’t increase/decrease at the same rate). Compare and Contrast Yards to Square Yards Number of Feet Area of Square (yd2) Yards to Feet Number of Yards Length of a Side of a Square Yard Tables: Linear or Nonlinear Is the rate of change constant (the same)? +2 +2 +2 x y 2 50 4 35 6 20 8 5 linear -15 -15 -15 +3 +3 +3 x y 1 1 4 16 7 49 10 100 nonlinear +15 +33 +51 Identify: Linear or Nonlinear Table? x y 0 20 5 16 10 12 15 8 linear x 0 2 4 6 y 0 2 8 18 nonlinear Graphs: Linear or Nonlinear Is the graph a straight line? linear nonlinear linear Identify: Linear or Nonlinear Graph? linear linear nonlinear Linear Nonlinear Identify:Linear or Nonlinear Equation? y = .6x1 y = x2 + 8 y = 3x 2 +1 Linear Nonlinear Linear (exponent is (exponent >1 ) 0 or 1) (y=mx+b form) y = 2/x + 5 Nonlinear (variable in the denominator) 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. Exit Slip Identify if linear or nonlinear. 1. Table A 3. Equation x 3 6 9 12 y 12 10 8 6 y = x8 + 5 2. Graph a b c Exit 1. What does linear mean? Ticket 2. Is the function linear or nonlinear? WHY OR WHY NOT? B A X Y X Y 1 6 -2 2 2 8 -1 4 3 10 0 8 4 12 1 16 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.