Math 170 functions data and models
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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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Math 170 functions data and models

Math 170 Functions, Data, and Models

Introduction and Functions

  • Paul Meyer Reimer, Guide


Basic concepts

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


Word examples

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.”


Table examples

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?


Formula examples

Formula Examples


Graph examples

Graph Examples

  • Describe the functions and non-functions displayed in the graph.


Math 170 functions data and models

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


Math 170 functions data and models

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


Math 170 functions data and models

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


Dependent independent variables

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.


Homework before thursday

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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