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

Objective: To be able to identify if a function is linear o not. Warm-Up:

Linear VS NON-LINEAR  Linear:  The rate of change is constant  The graph appears to be a straight line When looking at an equation:  x and y in the equation both have exponents of 0 or 1 (equation)  x and y are NOT multiplied together (equation)  x and y DO NOT appear in the denominator, exponents, or radical signs (equation)

Linear vs. Non-Linear:  Non-Linear: The rate of change is NOT constant The graph IS NOT a straight line

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 (yd 2 )

Graphs: Linear or Nonlinear  Is the graph a straight line?  linear  nonlinear

Identify: Linear or Nonlinear Graph?  linear  nonlinear

Equations: Linear or Nonlinear  REMEMBER: x 1 = x and x 0 = 1 y = x + 4 y = 6/x y = 4 y = x y = ½ x linear nonlinear linear nonlinear linear

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

Tables: Linear or Nonlinear  linear  nonlinear xy xy  Is the rate of change constant (the same)? **Constant change in the x value and y value**

Identify: Linear or Nonlinear Table? xy x0246 y02818  linear  nonlinear

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.

What is SLOPE?  Can non-linear functions have a slope?

4 types of slope (Same as Rate of Change) Uphill, left to right Downhill, left to right

Determine Slope Given a Graph:

When does it hit the next whole value!

If given 2 points on a line, you may find the slope using the formula m = y 2 – y 1 x 2 – x 1

3) Find the slope of the line that goes through the points (-5, 3) and (2, 1).

Find the slope of the line that passes through (3, 5) and (-1, 4) ¼ 4.- ¼

Find the slope given the table: X2222 Y0135 Chose any 2 points on the line, and use the slope formula to find the slope.

Find the slope given a table X0256 Y151113

Slope Day 2 

Finding the missing coordinate: Given the ordered pairs (1,y) and (2,3) and m= -4

Finding the missing coordinate: Given the ordered pairs (x,-3) and (2,6) and m= -1

Exit Slip  Identify if linear or nonlinear. 1.Table A 2.Graph 3.Equation x36912 y 1086 abc y = x

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.