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Represent Functions as Rules and Tables

This section introduces the concept of functions in algebra and calculus. Learn about defining functions, independent and dependent variables, domain and range, and how to create tables.

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Represent Functions as Rules and Tables

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  1. Represent Functions as Rules and Tables Section 1.6

  2. Test on Tuesday

  3. The Concept • Thus far we’ve been dealing with the basics of one-line expressions and equations • Today we’re going to take a bit if a departure and instead look at something called functions • In order to do this we’ll introduce some new terminology and way of expressing functions

  4. The function Most of our work in Algebra and Calculus is based on the concept of a function Function: An equation that relates an independent variable (input) to a dependent variable (output) such that each independent variable is paired with exactly one dependent variable. ????

  5. The function machine The easiest way for us to think of a function is through this diagram Each x put into the machine, yields a specific y. Function

  6. Yes or No? Due to the nature of a function, we can often determine if a set of numbers is a function based on their inputs and outputs e.g. Axis of symmetry Vertex

  7. DDR…or…D&R Each function has a set of inputs and outputs over which it is defined. The set of inputs (x) is called the Domain The set of outputs (y) is called the Range Domain Range Axis of symmetry Vertex

  8. Making a Table We can also reverse our process, given a function. e.g. Make a table for the function y=3x+1 given the domain below Axis of symmetry Vertex

  9. Making a Table We can also reverse our process, given a function. e.g. Make a table for the function y=-2x-1 given the domain below Axis of symmetry Vertex

  10. Making a Table We can also reverse our process, given a function. e.g. Make a table for the function y=x-1 given the RANGE below Axis of symmetry Vertex

  11. Make a rule Make a rule compare the domain and range and make a function e.g. Axis of symmetry Vertex

  12. On Your Own Algebraic Toys has created a line of Mathematician action figures that you want to buy. Each figure costs $15.72. You for sure want to buy the Newton figure with the falling apple and the Galileo with ankle cuff, but are unsure about the cost of buying more. Make a table that represents the amount spent on these figures starting with the first two and up to a total of 8.

  13. Most Important Points • Defining a function • Independent variable vs. dependent variable • Domain and Range • Making a table

  14. Homework 1.6 Pg. 38 • 1-8, 13-21, 24

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