Linear vs Nonlinear Functions

Table of Contents 46: Warm-Up 47: What is the Difference Between Linear and Non Linear Functions?

Warm-Up State slope-intercept form What does “m” represent? What does “b” represent? Linear functions have a constant rate of change. What does this mean? Describe what a graph of a linear function looks like.

Learning Intention/Success Criteria LI: We are learning how to tell the difference between linear and nonlinear functions SC: I know how to -recognize the standard form of a quadratic function -recognize that quadratic functions yield parabolic graphs -tell the difference between linear and nonlinear equations and graphs

EQ: What is the Difference Between Linear and Non Linear Functions? 1/15/2019

Linear When graphed, it is a straight line The output (y) changes at a constant rate as the input (x) changes The highest exponent on any variable is 1

Nonlinear When graphed, it is not a straight line The output (y) does not change at a constant rate as the input (x) changes There is at least one exponent in the equation that is greater than or equal to 2.

Parabola A “U” shaped or an upside down “U” shaped graph Coefficient The number in front of a variable Quadratic Function A function written: F(x) = Ax2 + Bx + C A, B, and C are coefficients, where A cannot equal zero Graphs a parabola The largest exponent in the equation is always 2.

Distinguish and Analyze 1. Distinguish between linear and nonlinear functions Analyze the graphs to answer the following: What are differences between the shapes of linear and nonlinear graphs? How is the symbolic representations of a linear function different from a nonlinear function?

Matching! 1. Keep your card face down until told to flip it over 2. On my go, flip your card over A. If you have an equation, look for someone with a “linear” or “nonlinear” card that matches your equation B. If you have a “linear” or “nonlinear” card, find someone with an equation that matches your word

Characteristics of Nonlinear 1. Do not turn over your paper until told 2. On EACH sticky note you use, please write your name and your partner(s) name in the bottom right corner 3. On the back of this page, you will see a set of graphs and their symbolic representations 4. Look this over with your partner

Characteristics of Nonlinear Continued 5. Your task is to write as many difference and similarities as you can a. Compare/contrast the graphs and write similarities/differences between them b. Compare/contrast the symbolic representations and write similarities/differences between them 6. You need at least 3 similarities or differences

Characteristics of Nonlinear Continued 7. Share with another group at your table and rewrite your answers to combine both groups’ ideas 8. At the end, have someone write up their answers on the whiteboard under the correct category.

Exit Note: 3, 2, 1 On a paper, write: 3 things you learned today 2 things you found interesting or would like to learn more about 1 thing you still have questions on Place your exit note in the jar before you leave.