4.3 Patterns and nonlinear functions

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4.3 Patterns and Non-Linear Functions:

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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

There is a connection/relationship between the area and the radius. 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. Pizza Area Sauce Cost Radius (in), r Area (in2), A 2 12.57 4 50.27 6 113.10 8 201.06 10 314.16 Weight(oz) , w Cost, C 2 $.80 4 $1.60 6 $2.40 8 $3.20 10 $4.00 Sauce Cost Pizza Area C O S T A R E (in2) 6 300 200 4 nonlinear 2 linear 100 0 2 4 6 8 10 0 2 4 6 8 10 Radius (in) 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. The total number of blocks y is the cube of the number of blocks on one edge x. graph Words: Equation: y = x3

2 1 2 2 2 4 2 3 8 2 4 16 2 5 32 2 6 64 2 7 128 2 8 256 1 2 1 2 2 4 3 2 9 4 2 16 5 2 25 6 2 36 7 2 49 8 2 64 1 3 1 2 3 8 3 3 27 4 3 64 5 3 125 6 3 216 7 3 343

y = 2x Writing a rule to describe a nonlinear function. X Y 1 2 4 3 8 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 Y 1 2 4 3 8 16 5 32 y = 2x

Assignment: Pg 250: 6-20, 26-29 Hint: a. 12-18 all have exponents in the equation. b. 14, 16 have fractions in your answer.