4 3 Patterns and nonlinear functions Identify and

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 There is a nonlinear? There is a connection/relationship Sauce Cost Pizza Area connection/ between the area and the relationship Radius (in), r Area (in 2), A radius. Weight(oz) , w Cost, C between the 2 12. 57 2 $. 80 cost and weight of 4 50. 27 4 $1. 60 the sauce. 6 113. 10 6 $2. 40 8 201. 06 8 $3. 20 10 314. 16 10 $4. 00 Sauce Cost Pizza Area A R E A 300 200 100 nonlinear C O S T 6 4 linear 2 (in 2) 0 2 4 6 8 10 Radius (in) 0 2 4 6 8 10 Weight (oz)

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. Words: The total number of blocks y is the cube of the number of blocks on one edge x. Equation: y = x 3 graph

1 4 9 16 25 36 49 64 81 100 1 8 27 64 125 216 343 121 144 169 196 225 256 Page 250: 6 -12, 27 -29 2 4 8 16 32 64 128 256

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= 2 4 x

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= x 2

Writing a rule to describe a nonlinear function. X 1 2 3 4 5 Y 6 12 24 48 96 y= x (3)2 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.