Question
Asked Nov 8, 2019

practice question 3 

3. Graph the following relations (Note that Z is the set of all integers and R represents
the set of all real numbers):
(a) {(r,y),yR, |2 + y] < 1}
13
15
(b) {(x, y)|,y Z,
-V10 y10
4
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3. Graph the following relations (Note that Z is the set of all integers and R represents the set of all real numbers): (a) {(r,y),yR, |2 + y] < 1} 13 15 (b) {(x, y)|,y Z, -V10 y10 4

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Expert Answer

Step 1

Hey, since there are multiple subparts posted, we will answer first question. If you want any specific question to be answered, then please submit that question only or specify the question number in your message

Given a relation

(x,y)lx,y E R, 12x+yl < 1}
To graph the given relation
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(x,y)lx,y E R, 12x+yl < 1} To graph the given relation

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Step 2

To start with the given inequality,

2xy1
By definition of absolute value of a function,
12x yl1 implies -1 2xy1
We consider the first inequality,
-1 2xy
Add 1 on both side of the equation to bring all terms on one side,
2x+ y+ 1
-1+1
0 2xy 1
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2xy1 By definition of absolute value of a function, 12x yl1 implies -1 2xy1 We consider the first inequality, -1 2xy Add 1 on both side of the equation to bring all terms on one side, 2x+ y+ 1 -1+1 0 2xy 1

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Step 3

To plot the g...

Now, we plot the inequality by plotting the graph for 2x y 1
shading the region to hold the inequality,
0 and then
2x y 0
2-
(-0.5, 0)
2
2
(0,-1)
-2
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Now, we plot the inequality by plotting the graph for 2x y 1 shading the region to hold the inequality, 0 and then 2x y 0 2- (-0.5, 0) 2 2 (0,-1) -2

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Math

Algebra

Equations and In-equations