# Nonlinear Functions & Set Theory

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© Copyright NewPath Learning. All Rights Reserved. 93-4710 www.newpathlearning.com A function is a rule that is performed on a number, called an input, to produce a result called an output. There are two types of functions: linear and nonlinear. Linear functions can be represented by straight lines on a coordinate plane. A linear function has an equation that can be written in the form of y = m x + b. Equations whose graphs are not straight lines are called nonlinear functions. Nonlinear Functions Set Theory A set is a collection of individual objects. Set theory helps us organize things into groups and to understand logic. Subset Definition Notation Example Venn Diagram Set A is a subset of set B if all the elements of set A are in set B. A B A B A B A = {apple, orange} B = {apple, orange, pear, banana} A B All the elements of A are in B. Intersection Definition Notation Example Venn Diagram The intersection of sets A and B consists of only elements which belong to both sets A and B. A B A = {apple, orange, plum} B = {pear, banana, apple} A B = {apple} Apple is the only fruit in both sets. The union of sets A and B consists of all elements which belong to either set A or set B. A B A = {apple, orange, plum} B = {pear, banana, apple} A B = {apple, orange, plum, pear, banana} All the elements in both sets are included. As a round balloon gets inflated, its radius changes and its volume increases. Radius (in.) Volume (in 3 ) 1 2 3 4 5 6 4.19 33.52 113.13 268.16 523.75 904.32 0 1 2 3 4 5 6 7 8 9 10 Radius (in.) V olume (in 3 ) 0 100 200 300 400 500 600 700 800 900 1,000 Sample Graphs of Nonlinear Functions A B Union Definition Notation Example Venn Diagram 4 4 3 3 2 2 1 1 -1 -1 -2 -2 -3 -3 -4 -4 0 4 4 3 3 2 2 1 1 -1 -1 -2 -2 -3 -3 -4 -4 0 Nonlinear Functions & Set Theory
© Copyright NewPath Learning. All Rights Reserved. 93-4710 www.newpathlearning.com A function is There are two types of functions: and . Linear functions can be represented by . A linear function has an equation that can be written in the form of . Equations whose graphs are not straight lines are called . Nonlinear Functions Set Theory A set is Subset Definition Notation Example Venn Diagram Intersection Definition Notation Example Venn Diagram As a round balloon gets inflated, its radius changes and its volume increases. Radius (in.) Volume (in 3 ) 1 2 3 4 5 6 4.19 33.52 113.13 268.16 523.75 904.32 0 1 2 3 4 5 6 7 8 9 10 Radius (in.) V olume (in 3 ) 0 100 200 300 400 500 600 700 800 900 1,000 Draw a Sample Graph of a Nonlinear Functions Union Definition Notation Example Venn Diagram 4 4 3 3 2 2 1 1 -1 -1 -2 -2 -3 -3 -4 -4 0 Key Vocabulary Terms coordinate plane equation function input intersection linear function nonlinear function output set set theory subset union . . . . . . Set theory helps us Nonlinear Functions & Set Theory \|xiBAHBDy01676sz\