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Math 170 Functions, Data, and Models

Math 170 Functions, Data, and Models. Introduction and Functions. Paul Meyer Reimer, Guide. Basic Concepts. What is a function? A rule that assigns to each possible input exactly one output A question: such that when asked to any one person there is only one answer

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Math 170 Functions, Data, and Models

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  1. Math 170 Functions, Data, and Models Introduction and Functions • Paul Meyer Reimer, Guide

  2. Basic Concepts • What is a function? • A rule that assigns to each possible input exactly one output • A question: such that when asked to any one person there is only one answer • What are domain and range? • The possible inputs and actual outputs • The possible people and their actual answers • How can functions be represented? • Words, tables, graphs, and formulas

  3. Word Examples • Who is your biological mother? • Who is your biological child? • Given the length, l (cm) of one side of a square, What is the area of the square (in square cm)? • Given a number, x, what is its square root? • The number of digits to the left of the decimal point of the decimal representation of a given number. • Paul’s distance from the podium a given number of seconds after he says, “Go.”

  4. Table Examples • Describe in words all possible functions • There are 6 ordered pairs of variables. • Milk cannot be the input – why not? • Is “price” at a particular time during the month or an average over the entire month, or something else?

  5. Formula Examples

  6. Graph Examples • Describe the functions and non-functions displayed in the graph.

  7. 1.Which one point can be removed from the Figure 1.1 to make it the graph of a function? • A • B • C • D • Any one of the previous ConcepTest • Section 1.1 •Question 1

  8. 3. The graph in Figure 1.2 remains the graph of a function when which of the following points are added • (0,0) • (-100,1) • (1,-100) • All of the above • (0,0) and (-100,1) ConcepTest • Section 1.1 •Question 3

  9. 8. Think of a (sans-serif) letter as the graph of some relationship on an x-y- coordinate system. How many (lower case) letters of the alphabet could be the graph of a function? • None • One • Two • Most of them • All of them ConcepTest • Section 1.1 •Question 8

  10. Dependent & Independent variables • The variable corresponding to the domain (the Year) is the independent variable. • The variable corresponding to the range (Time) is the dependent variable.

  11. Homework Before Thursday • Read Syllabus & Section 1.1 (if not already done). • Complete Moodle First Survey. • Complete WileyPlus S1.1 assignment. • Read Section 1.2.

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