Understanding the Viewing Rectangle/Window of the Graphing Calculator 1.1 and Part of 1.2 Understanding the Viewing Rectangle/Window of the Graphing Calculator Domain and Range of a Relation Determining Whether a Relation is a Function Determining Whether an Equation is a Function Pg. 135 # 30 and 32 Pg. 149 # 2-22 even

On a Texas Instruments graphing calculator, the “Viewing Rectangle”, also known as the “Viewing Window” is the part of the xy-coordinate system that is shown when you push the “GRAPH” button. Pushing the “WINDOW” you see seven value settings: Xmin – the smallest X value (on the left side) in the graph window Xmax – the largest X value (on the right side) in the graph window Xscl – the x axis tick marks occur at multiples of this number For example, if the Xscl was set at 2, the tick marks would indicate the numbers 2, 4, 6, 8, 10, etc… going right and -2, -4, -6, -8, -10, etc….going left. Ymin – the smallest Y value (at the bottom of the screen) in the graph window Ymax – the largest Y value (at the top of the screen) in the graph window Yscl – the y axis tick marks occur at multiples of this number Xres – this can be any number 1 – 8. It determines the resolution. When graphs are drawn, it uses all the pixels on the screen when graphing at Xres = 1. It uses every second pixel on the screen when Xres = 2. Every third pixel is used when Xres = 3. And so on… It is recommended that you leave this setting at Xres = 1

What is the meaning of the following window settings: [-100, 100, 50] by [-150, 150, 10] ? Open your book to page 135 and determine the correct matches for #29 and #31.

A Relation is any set of ordered pairs. Relations are easy to understand if you think of them as pairs of identifying words and/or numbers that belong together in some context. For example, { (aluminum, 25), (plastic, 8), (paper, 19) } could represent the total pounds of recycling materials your family generated this week broken into categories. The first set of components - aluminum, plastic, and paper – is the Domain. The second set of components – 25, 8, and 19 – is the Range. Identify the Domain and Range of this Relation: { (5, 12), (10, 16), (15, 18), (20, 21), (25, 22) }

A Relation is Defined as a Function if each element in the domain has only one assigned match in the range. Note: It does not matter how the range elements are paired. Determine whether each relation is a function: { (1, 2), (3, 4), (5, 6), (5, 8) } { (1, 2), (3, 4), (6, 5), (8, 5) }

If the y variable in an equation is raised to any even power – y2, y4, y6, etc…- then the equation is NOT a function. When you take such an equation and solve for y, you have to take an even numbered root of both sides. This generates two or more values of y for each x value that may be introduced. Thus, the rule of having each x (domain) value paired with only one y (range) value is broken and the equation is not a function. Solve each equation for y and then determine whether the equation defines y as a function of x: 2x + y = 6 6. x2 + y2 = 1 What form do these two equations take when graphed? Does visualizing the graphs help in determining if they are a function?