## Nonlinear Functions and Set Theory

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#### Study Guide Nonlinear Functions and Set Theory Mathematics, Grade 7

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NONLINEAR FUNCTIONS AND SET THEORY A function can be in the form of y = mx + b. This is an equation of a line, so it is said to be a linear function. Nonlinear functions are functions that are not straight lines. Some examples of nonlinear functions are exponential functions and parabolic functions. o An exponential function, y = aˆx, is a curved line that gets closer to but does not touch the x-axis. o A parabolic function, y = ax² + bx +c, is a U-shaped line that can either be facing up or facing down. Graphs can be used to represent different situations, like a drive on a trip or a ball thrown into the air. In these cases, it is important to read a graph correctly. A graph can also be used to compare two rates. Rates are fractions in which the numerator and denominator have different units of measure. o Rates of change refer to a change in the numerator over a change in time. Rates of change are often used in calculating speed, such as miles per hour, feet per second, or words per minute. Set theory refers to a collection of objects in a set and how it can be displayed or manipulated. o A Venn diagram displays data in circles showing how much data is in a certain category and how much data overlaps the categories. © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.
How to use nonlinear functions and set theory Nonlinear functions need to be recognized on a graph. The figures below show the two types of nonlinear functions. Exponential function Parabolic function y = aˆx y = ax² + bx +c The y values for any function, whether linear or nonlinear, can be found by plugging in the x values and evaluating the function. Graphs can be used to represent many situations. o A line that goes up means an increase of some sort, like an increase of movement, a ball moving upwards, or a car driving. o A horizontal line means no change, like a car that is stopped. o A line that goes down means a decrease of some sort; like a decline in speed or temperature. When a graph has two lines that cross, it shows where the two equations are equal. © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.
Rates can be used with speed. If Jon drove 594 miles in 11 hours, his rate of speed would be 54 miles per hour. When comparing two objects with different rates of speed such as miles per hour and feet per second, the rates can be changed as follows: Ex. x miles x 1 hour x 1 minute x 5280 feet = (x)(5280) feet 1 hour 60 min. 60 sec. 1 mile (60)(60) sec. In the equation, the hours, the minutes and the miles cancel out to leave feet per second with the numbers. So to change 2 mph into ft per second, the answer would be (2)(5280) feet/ (60)(60) seconds or 10,560 ft/3,600 seconds or 2.93 ft/sec. Set theory is helpful to display an analyze data. With a Venn diagram, the data is displayed in circles showing how much data is in a certain category. The Venn diagram below shows how many people like only pizza, only subs, or both. The total number of people asked is 33. A set has the notation: set A = {x >12}, s o for the set of people who like only pizza, the set notation would be, set Only Pizza = {x = 12}. Venn diagrams also can have more than one circle to represent three categories. © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.
Try This! What kind of function is y = aˆx? What kind of function is y = ax² + bx + c? A graph of Joan riding her bike shows a straight horizontal line for two hours. What could that mean? If Roberto can type 150 words in 9 minutes, how many words can he type per minute? What is 12 mph changed to feet per second? Make a Venn diagram that shows: o people who like only vegetable juice- 5 o people who like only milk- 10 o people who like both- 4 © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.