11-17-15 AM4.2a To Graph Inequalities and Systems of Inequalities in Two Variables Part 1 Reset your calculator

2. How do you know, by looking at y > 2x + 3 , where to shade? To graph y > 2x + 3 is bigger than 1. Start with Y1 = 2x + 3 the line. Answer 2. How do you know, by looking at y > 2x + 3 , where to shade? -10 10 -10 10 TRUE FALSE 3. What should be the lower boundary? Y1 4. What should be the upper boundary? 10

*Use ZOOM, 6:ZStandard to get a 20 x 20 window. COPY: To clear a drawing: -Go to Home Screen (2nd QUIT) -2nd PRGM (DRAW) -Choose #1 (CLRDRAW); ENTER again. You must use it EVERY time unless you want more than one graph. [SHADE is 2nd PRGM, Choose #7] [Y1: VARS Y-VARS FUNCTION Y1] [The comma is above the “7“ ]

COPY: Luxury Model for shading: SHADE( lower, upper, left, right, Direction, Resolution) Direction: 1) 2) 3) 4) Resolution: 1) Draws every line. 2) Draws every 2nd line. 3) Draws every 3rd line. 8) Draws every 8th line.

In the following command line, what does each item do? Shade(Y1, 10, -10, 10, 2, 4) for Y1 > 2x + 3 lower upper left right direction resolution Now, follow me as I put it into the graphing calculator and see what you get. Use Y1 = 2x + 3, ZOOM, 6:ZStandard Use 2nd QUIT to get to the Home Screen. ClrDraw Shade(Y1, 10, -10, 10, 2, 4) When you get it to work, change the direction and resolution to see what they do!

Where did this boundary come from? What effect did the -10 & 10 have on the graph?

Shade(Y1, 10, -10, 10, 2, 3) Let’s graph Y1 > - x – 5 First step? CLR DRAW & GRAPH Y1 = - x – 5 Next step? Look at it and decide what is the lower bound and what is the upper bound -10 10 -10 10 Shade? You choose the direction and resolution. Shade(Y1, 10, -10, 10, 2, 3)

Shade(-10, Y1, -10, 10, 2, 3) Let’s graph Y1 < x2 + 2 First step? CLR DRAW & GRAPH Y1 = x2 + 2 Next step? Look at it and decide what is the lower bound and what is the upper bound -10 10 -10 10 Shade? You choose the direction and resolution. Shade(-10, Y1, -10, 10, 2, 3)

11-18-15 AM4.2a To Graph Inequalities and Systems of Inequalities in Two Variables Part 2 Reset your calculator OPENER: Graph y > x2 – 1 using the SHADE codes. (CLR DRW!)

Graph y > x2 – 1 Shade(Y1, 10, -10, 10, 3, 3) First step? CLR DRAW & GRAPH Y1 = x2 – 1 Next step? Look at it and decide what is the lower bound and what is the upper bound -10 10 -10 10 Shade? You choose the direction and resolution. Shade(Y1, 10, -10, 10, 3, 3)

We are taking what we learned yesterday and building on it We are taking what we learned yesterday and building on it. We will now show the intersection of two inequalities. Remember, calculators always work from the lowest values to the highest. That is, bottom to top, left to right. In Linear Programming, which we will work on later, the inequalities form a “Region of Feasibility.” This region is a polygon whose verticies predict the maximum profits for businesses. Doesn’t that sound interesting! Do inequalities have any connection to our everyday lives? Absolutely! Every time we think in terms of “at least” or “at most”, we are describing an inequality!

To recap: To clear a drawing: -Go to Home Screen (2nd QUIT) -2nd PRGM (DRAW) -Choose #1 (CLRDRAW); ENTER again. You must use it EVERY time unless you want more than one graph. In the following command line, what does each item do? Shade(Y1, 10, -10, 10, 2, 4) for Y1 > 2x + 3 lower upper left right direction resolution

Now, let’s add a little more: 1st step Set up Y1 & Y2 and graph. CLRDRAW 2nd step: Let’s see where we want to shade Four distinct regions are created.

What does each region mean? Can you find a shortcut? 10 Lower? Y1 Upper? 10 -10 10 Lower? -10 Upper? Y2 -10 Now, how should we put these into the calculator? Y1 only (Press ENTER) Both Neither (Press ENTER) Y2 only (Press ENTER) Separately & different directions! What does each region mean? Can you find a shortcut? The points are true for…

Why, yes, there is a shorter way! MOST of the time, you can use this method, but only if there is only one region being intersected AND one is > and the other is <. Otherwise, use two SHADE commands

Try this one on your own: (Use different values for each direction and do not use 1 for the resolution.) SHADE( lower, upper, left, right, direction, resolution) Alternately:

Difficulty Level? Everyone must vote: “1” for easy, “5” for hard Active Learning Assignment: Work on worksheet. You will work with your group and help each other. It starts easy, but uses higher order thinking skills to build knowledge as it goes on. Try something. If it doesn’t work, that is a learning experience, too! This is a class activity. If you do not finish in class, you can fill out the blanks for homework, and use www.desmos.com. Tomorrow will check them in class. Fill out your Exit Ticket and turn in tomorrow. TEST: Fri., Nov. 20, 2015