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Basic Math: Functions Name: ____TEACHER COPY ______________ CCSS.Math.Content.8.F.A.2 Date: ______________________ Period: _____ Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Lesson Plan: 1. Hook (adapted from: jokes4us.com): Mom/Dad: Did you work on your algebra homework at the family reunion? Kid: Yep, it was a function with relations. 2. Introduction and Vocabulary: In order to understand and identify functions, we need to first discuss the differences between certain sets of ordered pairs. A relation is a set of ordered pairs. The first elements of the ordered pairs are the inputs. All of the inputs together form a set called the domain. The second elements of the ordered pairs are the outputs. All of the outputs together form a set called the range. A function is a special type of relation where each input is paired with exactly one output. 3. Guided Practice: Work through problems 1-3 on the front of the worksheet. These deal with comparing two relations/functions. If time, students may complete the back of the worksheet dealing with more complex functions/equations. 4. Independent Practice (or partners): A. Give your own example of a function. Show it in a map, table, or graph. B. Give an example of a relation that is not a function. Show it in a map, table, or graph. C. Explain why the relation in problem 2 is not a function. 5. Exit Slip: Explain how you could use the vertical line test to see if a certain graph is a function. Licensed under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. All Rights Reserved by NewMathTeacher.Net Basic Math: Functions Name: __________________________________ CCSS.Math.Content.8.F.A.2 Date: ______________________ Period: _____ Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). A relation is a pairing of numbers in one set, called the domain (x's), with numbers in another set, called the range (y's). Each number in the domain is an input. Each number in the range is an output. 1. Indentifying Domain and Range. Mrs. Dournaee measured the growth of her tomato plants over five weeks. Identify the domain and range of the relation. Tomato Plant #1 Week Number (weeks), x Plant Height (inches), y Tomato Plant #2 1 2 0.5 1.5 3 4 4 9 5 15 Domain: Range: Week Number (weeks), x Plant Height (inches), y 1 2 0.25 1 3 3 4 7 5 12 Domain: Range: 2. Representing a Relation Represent the relation (-7, 2), (-6, 0), (-5, -1), (-5, -3), (-2, 1), (1, 1) as a graph and then as a mapping diagram. Graph: Mapping Diagram: INPUT OUTPUT A relation is a function if for each input there is exactly one output (x's are unique). When a relation is represented by a graph, you can use the vertical line test to tell whether the relation is a function. 3. Identifying Functions Are the relations from #1 also functions? Explain your reasoning. Is the relation from #2 also a function? Explain your reasoning. BONUS: Fill in the blanks for these functions. x -4 -3 -2 -1 0 1 2 3 4 5 y -1 1 3 5 7 x y -4 -3 -2 3 -1 0 5 1 2 3 Licensed under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. All Rights Reserved by NewMathTeacher.Net 4 9 5 Basic Math: Functions Name: __________________________________ CCSS.Math.Content.8.F.A.2 Date: ______________________ Period: _____ Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). 1. Checking a Solution of an Equation in Two Variables A. Tell whether (-1, 3) is a solution of 5x + 6y = 10. B. Tell whether (-1, 3) is a solution of 5x + 6y = 13. 2. Finding Solutions of an Equation in Two Variables Vanessa is saving money for an iPod. So far, she has $40 saved. For every child she babysits, she earns $20. Use the equation y = 20x + 40, where y represents the total she's saved and x is the number of children she's babysat. Make a table of solutions for the equation and then tell how many children Vanessa will have to babysit to save a total of $400? First, use a T-chart to find specific values. x Next, find the value of x when y = 400. y 0 10 25 3. Graphing a Linear Equation using a Table of Solutions Write 4y - 12x = 8 in function form. Then graph the equation using a table of solutions. x y -2 0 2 4. Graphing Horizontal and Vertical Lines Graph x = -2. Graph y = 3. Licensed under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. All Rights Reserved by NewMathTeacher.Net