Intermediate Algebra – Student Workbook – Second Edition 2013

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$Lesson 2a – Assessment - Scottsdale Community College - Math Blog$

Lesson 1a – Introduction to Functions Mini-Lesson Problem 5 WORKED EXAMPLE – DETERMINE FUNCTIONAL RELATIONSHIPS USING MULTIPLE REPRESENTATIONS The table below shows 3 different representations for two relationships. Determine which relationship defines a function. Data Set Relationship 1 Relationship 2 x -4 -2 0 3 5 y 1 3 5 8 10 OR x y -4 1 -2 3 0 5 3 8 5 10 x 0 1 1 4 4 y 0 1 -1 2 -2 OR x y 0 0 1 1 1 -1 4 2 4 -2 Set of Ordered Pairs Graph All input values are associated with one, unique output value. {(-4, 1), (-2, 3), (0, 5), (3, 8), (5, 10)} No input value is repeated in an ordered pair. Two of the listed input values (1 & 4) are associated with more than one output value. {(0, 0), (1, 1), (1, -1), (4, 2), (4, -2)} Two of the listed input values (1 & 4) are associated with more than one output value. No vertical line intersects the graph in more than one point. We say the graph PASSES the VERTICAL LINE TEST. Vertical lines intersect the graph at more than one point meaning inputs are repeated with different outputs. We say that the graph FAILS the VERTICAL LINE TEST. Function? YES NO Scottsdale Community College Page 6 Intermediate Algebra
Lesson 1a – Introduction to Functions Mini-Lesson Function Notation: FUNCTION NOTATION is used to indicate a functional relationship between two quantities as follows: y = f(x) means that y is a function of x read y = f(x) as “y equals f of x” Problem 6 MEDIA EXAMPLE – UNDERSTANDING APPLICATIONS OF FUNCTIONS Suppose that the cost to fill your 15-gallon gas tank is determined by the function C(g) = 3.29g where C is the output (cost in $) and g is the input (gallons of gas). a) Graph this function using your calculator. [Go to Y= and type 3.29x into the Y1 slot. Then, press WINDOW and enter xmin = 0, xmax =20, ymin = 0, and ymax=70 then press GRAPH]. Show a good graph in the space below. b) Use the Table feature of your graph and identify the first and last ordered pairs that are on the graph (based on the information above). [2 nd >Graph will take you to the table]. Include both ordered pairs and function notation. c) What is the INPUT quantity (including units) for this function? Name the smallest and largest possible input quantity then use this information to identify the PRACTICAL DOMAIN. d) What is the OUTPUT quantity (including units) for this function? Name the smallest and largest possible output quantity then use this information to identify the PRACTICAL RANGE. Scottsdale Community College Page 7 Intermediate Algebra
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Appendix A: You Try Answers Lesson
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Intermediate Algebra – Student Workbook – Second Edition 2013

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