The discussion revolves around sketching a region in ℝ² defined by the inequalities -2 ≤ x ≤ 4 and y ≤ 2. Participants are attempting to visualize the area that satisfies these conditions, focusing on how to accurately represent the boundaries and shaded regions on a graph.
There is an ongoing exploration of how to correctly sketch the region, with some participants receiving guidance on the boundaries and the nature of the region. Multiple interpretations of the problem are being discussed, particularly regarding the representation of the boundaries and the area to be shaded.
Some participants express confusion about the boundaries, particularly regarding the use of the x-axis as a boundary and the implications of the inequalities. There is also mention of a lack of figures in some cases, which may affect the clarity of their understanding.
Chewybakas said:Homework Statement
I have to sketch the following region in R^2 but i Have no idea how to do it!
Homework Equations
S1 = {(x; y) εℝ^2 : -2≤x≤4 y,≤2}
The Attempt at a Solution
I plotted the line from -2 to 4 on the x-axis and a line greater then 2 from the y-axis but i am sure i am doing this incorrectly! any help is appreciated!
Chewybakas said:So if i plot those points and draw the lines i get a rectangular shape on my graph is that the correct solution?
This is not a useful description. The region is unbounded in one direction. It is bounded on three sides by straight lines. A better description would tell us what the three boundary lines are and maybe what the points at the corners are.Chewybakas said:I have a graph with an x and y axis, the points drawn in and lines from each point, where the line y=2 intersects the x points i shade in the rectangular shape. If I am wrong could you please tell me what to do!
-2≤x≤4. Draw two vertical lines at x= -2 and at x= 4 so that the "line from -2 to 4 on the x axis" is inside them. I don't know what you mean by "a line greater than 2 from the y-axis". y≤2 is all y less than or equal to 2 so draw a horizontal line at y= 2 crossing those two vertical lines. The region you want to shade is the area below that horizontal line and between the two vertical lines. Because there is no lower limit on y, there is no lower boundary- the region you want is the "infinite strip" between the vertical lines and below the horizontal line.Chewybakas said:Homework Statement
I have to sketch the following region in R^2 but i Have no idea how to do it!
Homework Equations
S1 = {(x; y) εℝ^2 : -2≤x≤4 y,≤2}
The Attempt at a Solution
I plotted the line from -2 to 4 on the x-axis and a line greater then 2 from the y-axis but i am sure i am doing this incorrectly! any help is appreciated!
Chewybakas said:Ahh that's where i was going wrong! I was using the x-axis itself as a boundary! I have no idea why! Thank you for clearing that up! But in this question i have no figures.
{(x; y) εℝ^2 : x≤y}
Is that just the x and y axis! thank you for all your help!
HallsofIvy said:-2≤x≤4. Draw two vertical lines at x= -2 and at x= 4 so that the "line from -2 to 4 on the x axis" is inside them. I don't know what you mean by "a line greater than 2 from the y-axis". y≤2 is all y less than or equal to 2 so draw a horizontal line at y= 2 crossing those two vertical lines. The region you want to shade is the area below that horizontal line and between the two vertical lines. Because there is no lower limit on y, there is no lower boundary- the region you want is the "infinite strip" between the vertical lines and below the horizontal line.