M 112 Short Course in Calculus Chapter 1 – Functions and Change Sections 1.1 – What is a Function? V. J. Motto

1.1 What is a Function? A function is used to represent the dependence of one quantity upon another. Daily low temperatures in International Falls, Minnesota Dec 17 – 21. Which variable is dependent on which variable? 10/29/2015 2

Mathematical Definition A function is a rule that takes certain numbers as inputs (domain) and assigns to each a definite (unique) output number (range). Date is the independent variable (input - domain) Temperature is the dependent variable (output – range) Rule of Four –describing functions Tables Graphs Formulas Words 10/29/2015 3

Function Notation We write y = f(t) to express the fact that y is a function of t. The independent variable is t The dependent variable is y. f is the name of the function In our study of functions we are always interested in the following: y-intercepts x-intercepts (or zeros) local maximum and minimum values points of inflection Where the function is increasing and decreasing 10/29/2015 4

Identify the features of this graph 10/29/2015 5

Mathematical Modeling This was the subject matter for M110 which is a prerequisite for this course. Lets use the data below to create a model. Winning height (approximate) for Men’s Olympic pole vault event. 10/29/2015 6

Modeling with the TI-83+/TI A quick review 10/29/ Enter the data The data plot The linear regression function The results of the function Data & Model