Graphing Simple Inequalities After watching the video above on graphing, you need to match the inequality statements below in the document below with their corresponding graphs.
In your wikispace journal, explain your entire thought process (from your first match to your last) and how you narrowed down the choices and knew which graph matched which inequality statement.
1. Less than or equal than sign so I knew it would be a closed circle over -2. 2. Open circle because there is no equal sign under the less than sign and over -2. 3. An "and inequality" so the solutions are in between -2 and 2. Also, one is open circle and a closed circle. 4. An "or inequality" so there will be two different lines.
3.2
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.
On both number lines and graphs one would be able to find the solutions very easily. On a graph it is just a matter if the shading is below or above the points. With a number line the solutions are found in between to points or a point continuing onto infiniti or negative infiniti. When x<=3 is represented on a number line one would need to have the circles closed since it is 'or equal to' sign. With a graph on x<=3 the line would be solid to show that any solutions found on the line can be solutions. y<2x+1 would be a dotted line, below the line with a yintercpet of 1 and 2/1 being the slope.
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.
inequality = y _< -1/2 + 4 (the less than is less than or equal to)
The shading is below the line which indicates that it would be a less than sign. The line is solid which means it would be less than or equal to. The y-intercept is positive 4 The slope 'rises' -1 and 'runs' over +2 to the right.
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?
Graphing Simple Inequalities After watching the video above on graphing, you need to match the inequality statements below in the document below with their corresponding graphs.
-Problems done in the document-
In your wikispace journal, explain your entire thought process (from your first match to your last) and how you narrowed down the choices and knew which graph matched which inequality statement.
1. Less than or equal than sign so I knew it would be a closed circle over -2.
2. Open circle because there is no equal sign under the less than sign and over -2.
3. An "and inequality" so the solutions are in between -2 and 2. Also, one is open circle and a closed circle.
4. An "or inequality" so there will be two different lines.
3.2
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.
On both number lines and graphs one would be able to find the solutions very easily. On a graph it is just a matter if the shading is below or above the points. With a number line the solutions are found in between to points or a point continuing onto infiniti or negative infiniti. When x<=3 is represented on a number line one would need to have the circles closed since it is 'or equal to' sign. With a graph on x<=3 the line would be solid to show that any solutions found on the line can be solutions. y<2x+1 would be a dotted line, below the line with a yintercpet of 1 and 2/1 being the slope.
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.
inequality = y _< -1/2 + 4
(the less than is less than or equal to)
The shading is below the line which indicates that it would be a less than sign.
The line is solid which means it would be less than or equal to.
The y-intercept is positive 4
The slope 'rises' -1 and 'runs' over +2 to the right.
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?
solution: (-5,5)
this is a solution because the system of inequalities have similar shading where that point lands.
solution to inequality f(x)>1/2+5: (1,6)
- to find weather or not a point is a solution to the system just plug it in to both inequalities and make sure both are mathematically correct.