Nonlinear Functions and Patterns in Mathematics
Discover and analyze patterns in nonlinear functions, interpreting graphs of linear and nonlinear functions, and writing rules to describe nonlinear functions. Explore relationships between variables in various mathematical contexts with practical examples and visual representations.
Download Presentation
Please find below an Image/Link to download the presentation.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author. If you encounter any issues during the download, it is possible that the publisher has removed the file from their server.
You are allowed to download the files provided on this website for personal or commercial use, subject to the condition that they are used lawfully. All files are the property of their respective owners.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author.
E N D
Presentation Transcript
4.3 Patterns and nonlinear functions Identify and represent patterns that describe nonlinear functions.
Interpreting graphs Linear function: a function whose graph is a nonvertical line. Nonlinear: a function whose graph is not a line
The area A, in square inches of a pizza is a function of its radius r, in inches. The cost C, in dollars, of the sauce for a pizza is a function of the weight w, in ounces, of sauce used. Graph these functions shown by the tables below. Is each function linear or nonlinear? There is a connection/relationship between the area and the radius. There is a connection/ relationship between the cost and weight of the sauce. Sauce Cost Pizza Area Radius (in), r Area (in2), A Weight(oz) , w Cost, C 2 12.57 2 $.80 4 50.27 4 $1.60 6 113.10 6 $2.40 8 201.06 8 $3.20 10 314.16 10 $4.00 Sauce Cost Pizza Area C O S T 6 A R E A (in2) 300 4 200 nonlinear 2 linear 100 0 2 4 6 8 10 Weight (oz) 0 2 4 6 8 10 Radius (in)
The table shows the total number of blocks in each figure below as a function of the number of blocks on one edge. What is a pattern you can use to complete the table Represent the relationship using words, an equation, and a graph. The total number of blocks y is the cube of the number of blocks on one edge x. graph Words: Equation: y = x3
12 22 32 42 52 62 72 82 1 4 21 22 23 24 25 26 27 28 2 13 9 1 4 16 23 33 43 53 63 73 8 8 25 27 16 36 64 32 49 125 64 64 216 128 92 102 112 122 132 142 152 162 81 343 256 100 121 144 Page 250: 6-12, 27-29 169 196 225 256
Writing a rule to describe a nonlinear function. The ordered pairs (0,0), (1,4), (2,16), (3,36), and (4,64) represent a function. What is a rule that represents this function? X 0 1 2 3 4 Y 0 4 16 36 64 y = 4x2
Writing a rule to describe a nonlinear function. The ordered pairs (1,2), (2,4), (3,8), (4,16), and (5,32) represent a function. What is a rule that represents this function? X 1 2 3 4 5 Y 2 4 8 16 32 y = 2x
Writing a rule to describe a nonlinear function. X 1 2 3 4 5 Y 6 12 24 48 96 y = (3)2x Page 250: 13-16; fractions on 14 and 16; exponents on all of them.
Assignment: Pg 249: 1-5, 12-16, 23,26 Skip 14 Hints: a. 12-18 all have exponents in the equation. b. 16 has a fraction or a decimal in your answer.
