Topic: Functions and Graphs I

Subtopic: Introduction to Graphing

**Overview**

Mathematics can be represented algebraically (with variables and equations as we have been doing), numerically (with tables of data), or graphically. It is this latter method on which we concentrate today. Concentrate on the graphing related terminology, then plotting points, then graphing lines via a "plug-n-chug" chart of points. By the end of this course you will be expert graphers analyzing mathematical applications by hand as well as by using a graphing calculator or related electronic graphing device. The next few sections of material are visually inspiring which is a pretty cool way to learn algebra!

**Objectives**

By the end of this topic you should know and be prepared to be tested on:

- 3.1.1 Signs of the x and y-coordinates of points in each of the four quadrants
- 3.1.2 Analyze graphs that represent real-life data by being able to answer questions about a real-life situation by "reading" a given graph of the data
- 3.1.3 Given the graph of a line find a point that lies upon it
- 3.1.4 Determine if a given point lies on a line given its equation or graph
- 3.1.5 Given the graph of a line find its x and y-intercept points
- 3.1.6 Given a set of points or chart of data points, plot the points and connect to form a line
- 3.1.7 Graph a line by the plug-n-chug method (a.k.a. point-plotting method), i.e., given a linear equation, form a chart of points that
- 3.1.8 Recognize that real-life data that grows (or falls) in a constant manner can be modeled by a linear equation

**Terminology**

Terms you should be able to define: x-axis, y-axis, axes, quadrant, origin, point, ordered pair, coordinates, axis-intercept point, plug-n-chug method (a.k.a. point-plotting)

**Text Notes**

This section covers some important terminology related to graphs and graphing. One process to get down well is graphing an equation by the plug-n-chug chart method. The charts of data points introduced in this section are often called plug-n-chug charts since you are plugging in x-values and chugging out y-values (or visa versa). This method may also be called "point-plotting". Either way it means to generate a table of points, plot them, and connect to form the line. This method is useful for graphing any equation not just lines!

If your text covers mathematical modeling you may find the examples interesting and/or motivating, but in my opinion they are too advanced for this level class and you may skip them.

**Supplementary Resources**

You will need access to a (free) online grapher, graphing software for your computer, or a handheld graphing calculator for the remainder of this class. These MathOL FAQs contain helpful info:

- Where can I find a free online grapher or graphing software?
- I want to purchase a handheld graphing calculator instead of using a free online grapher. Which calculator should I buy?
- I need a tutorial on how to use my graphing calculator.

- Some MML questions require you to produce a graph using MML's graphing tool. Pearson's Graphing Tool Help teaches you how to use it.
- Where can I find online some free printable graph paper?

More resources will be provided in class. Join the graphing threads on the class discussion board for graphing guides and examples to help you get started with your grapher!