Unit+3+Journal

Unit 3: Inequalities

__ 3.1: __
After watching the video above on graphing, you need to match the inequality statements below in the document below with their corresponding graphs.
 * [|Graphing Simple Inequalities] **

1. D 2. A 3.C 4.E 5.F 6.B

I knew #1 matched with graph D, because x was greater than or equal to -2, which meant that that circle had to be closed, and the arrow had to be going to the right. I knew #2 matched with graph A, because x was less than -2 which meant that the cirlce had to be open and going to the left. I knew that #3 matched with graph C, because x was greater than -2 and less then equal to 2, which meant that the circle on -2 would be open and the circle on 2 would be closed, and the lines would connect. I knew #4 matched with graph E, because x was greater than or equal to 2 or less than -2, which meant that the circle on 2 would be closed and going to the right, and the circle on -2 would be open and going to the left. I knew that #5 matched with graph F, because x was greater than or equal to -2 and less than equal to 2, which meant that the circle on -2 would be closed and going to the right, and the circle on 2 would be closed and going to the left, and the lines would join. I knew that #6 matched with graph B, because x was greater than 2 or less than equal to -2, which meant that the circle on 2 would be open and going to the right, and the circle on -2 would be closed and going the opposite way to the left.

__ **Summarize what we did in class today.** __ Explain what similar features are shown in the graph x>5 as you would graph it on a number line and x>5 as you would graph it on a coordinate plane. Also explain the similarities of x<=3 as graphed on a number line and x<=3 on a coordinate plane. Explain how this same thinking applies to y<2x+1 ?? How do you know which side of the line should be shaded since the line is slanted? Be sure to explain the short-cut method as well as the algebraic method you could use to prove that the correct side of the line has been shaded.

x>5 on a number line would have an open circle over 5, going to the right. On a coordinate plane, x>5 would be a dotted line thats shaded above. The open circle on a number line represents a dotted line on a coordinate plane. X<=3 on a number line would have a closed circle above 3 going to the left. On a coordinate plane, x<=3 would have a solid line shaded below. The sane thinking applies to y<2x+1, because is < which means that it will be a dashed line, and shaded below. If its > or >=, the line is shaded above, and if it's < or <=, the line is shaded below. To prove which side of the line that has to be shaded, you can pick a point on the coordinate plane from the shaded region, and plug the coordinates into the inequality.

__ 3.3: __
__ **(Looking at graph on page 113)** __ Write the inequality whose graph is shown. Explain every step of your thinking and how you came up with the inequality. y<= -1/2+4 First, i looked for the mx+b. I found that the Y intercept was 4, and the slope was -1/2, because it was going down to the right and up to the left. Then, i looked at the kind of line that was shown, and where the shading was. It was a solid line and was shaded below, which meant that it was <=.

__ **3.4:** __
Looking at the shaded graph in the document below, you need to identify a point that is a solution to the system and explain how you know it is a solution by looking at the graph. Also, identify a point that is a solution to only one of the inequalities, but NOT a solution to the system. Explain how you might test a point to determine whether it is a solution to the system or not?

A point that is a solution to the system is (-5,5) I know its a solution by looking at the graph, because it is in the purple shaded region, which is where both lines have solutions that are the same. (5,10) is solution to f(x)>1/2x+5 but not a solution to g(x)<= -3x-1. To see if a point is a solution to the system or not, you the the x and y values in the point and plug them into both inequalities. If the statement is true for one but false for the other, then the point is not a solution. If the statement is true for both inequalities, then the point IS a solution to the system.