Unit+3+Journals

__3.1:__

1) x ≥ -2 g oes with graph D  2) x < -2 goes with graph A  3) -2 < x ≤ 2 goes with graph C 4) x ≥ 2 or x < -2 goes with graph E 5) -2 ≤ x ≤ 2 goes with graph F 6) x > 2 or x ≤ -2 goes with graph B

The first thing I did to match each inequality with its graph was look at the sign. So I looked at number 1 and saw that it was ≥ which means the circle on the graph would be colored in. Then I looked for the number line that had -2 with a colored in circle above it and saw that Graph D had that and also the arrow was going in the right direction. For the second inequality, I looked for the number line that had an open circle above -2 and the arrow was pointing to the negatives which is Graph A. For number 3 I looked for one number line that had only one line with both a greater than and less than symbol and the only number line that has that is C. For number 4, I would need to match the inequality with a number line that had two different lines because it had "or" in the sentence. I narrowed it down to B and E since those are the only number lines that have two different lines on them. I knew the graph that corrseponds with the fourth inequality is E because it shows all the values greater than or equal to two and it also shows all the values less than -2. For number 5, I knew the graph would have to have only one line and since the other option had to different lines I knew it had to be F. And for the last inequality, the graph had to have two lines on the graph and B was the only one left.

__3.2:__ In class we were given four different equations and practiced drawing the lines on graphs. When graphing x>5 on a number line, you would find 5 and draw an open circle above it because the inequality does not include 5. Then you would draw a line with an arrow to the right because it is all the number greater than 5. On a graph,you would find 5 on the x axis and draw a vertical line. The line would be dotted because it does not include 5. Then you would shade everything to the right of 5 to include all of the values greater than 5. X ≤ 3 on a numberline would have a closed circle above the 3 and on the graph it would have a solid line which indicates that the 3 is included in the inequality. On the number line, the arrow would point to the left because it is all the numbers less than or equal to three and on the graph you would shade in the quadrants on the left because those are all the numbers less than or equal to 3. For y < 2x +1, plot a circle on the 1 on the y-axis because 1 is the y intercept and go up 2 and over to the right 1 since the slope is 2. Once you draw the line, you have to find all the variables less than 2x+1 so I think all the numbers left of the line would be shaded. To prove that the correct side of the line has been shaded, you could just plug in any values into the x and y variables to see if it works. Also, to be sure you shaded in the right side you could just look at the inequality and see that the symbol is a less than sign which means all the values less than 2x+1 which means on the values to the left of the line.