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Graphing the Intersection of Regions>
Graphing the Intersection of Regions 1Graphing the Intersection of Regions 1
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Question 1 of 4
1. Question
Graph the intersection of regions:`y≤2-x`$$y>x$$Hint
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Remember the following notations when graphing inequalities.Symbol Solid / Dotted `<` Dotted Line `>` Dotted Line `≤` Solid Line `≥` Solid Line First, treat the inequality sign as an equals sign and plot the curve.Graph the line `y=x`
Use a test point to see which side of the line is to be shaded. We can try `(``-2``,``0``)``y` `>` `x` `0` `>` `-2` Substitute `(-2,0)` The inequality is true, so we will shade the side of the line which includes the point `(-2,0)`
Next, graph the line `y=2-x`
Use a test point to see which side of the line is to be shaded. We can try the origin, `(``0``,``0``)``y` `≤` `2-``x` `0` `≤` `2-``0` Substitute `(0,0)` `0` `≤` `2` The inequality is true, so we will shade the side of the line which includes the origin
Finally, shade the overlapping regions.
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Question 2 of 4
2. Question
Graph the intersection of regions`2x+3y≤6`$$x<1$$Hint
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Remember the following notations when graphing inequalities.Symbol Solid / Dotted `<` Dotted Line `>` Dotted Line `≤` Solid Line `≥` Solid Line First, treat the inequality sign as an equals sign and plot the curve.Graph the line `x=1`
Since `x<1`, we can determine that the shaded part would be the left side because all values on the left side are less than `1`
Next, graph the line `2x+3y=6`
Use a test point to see which side of the line is to be shaded. We can try the origin, `(``0``,``0``)``2``x``+3``y` `≤` `6` `2(``0``)+3(``0``)` `≤` `6` Substitute `(0,0)` `0` `≤` `6` The inequality is true, so we will shade the side of the line which includes the origin
Finally, shade the overlapping regions.
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Question 3 of 4
3. Question
Graph the intersection of regions`y≥x^2`$$x+y<2$$Hint
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Excellent!
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Remember the following notations when graphing inequalities.Symbol Solid / Dotted `<` Dotted Line `>` Dotted Line `≤` Solid Line `≥` Solid Line First, treat the inequality sign as an equals sign and plot the curve.Graph the line `x+y=2`
Use a test point to see which side of the line is to be shaded. We can try the origin, `(``0``,``0``)``x``+``y` `<` `6` `0``+``0` `<` `6` Substitute `(0,0)` `0` `<` `6` The inequality is true, so we will shade the side of the line which includes the origin
Next, graph the curve `y=x^2`
Use a test point to see which side of the line is to be shaded. We can try the point `(``0``,``2``)``y` `≥` $$\color{#9a00c7}{x}^2$$ `2` `≥` $$\color{#9a00c7}{0}^2$$ Substitute `(0,0)` `2` `≥` `0` The inequality is true, so we will shade the side of the line which includes the point `(0,2)`
Finally, shade the overlapping regions.
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Question 4 of 4
4. Question
Graph the intersection of regions$$x>-1$$`y≤2x-1`Hint
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Fantastic!
Incorrect
Remember the following notations when graphing inequalities.Symbol Solid / Dotted `<` Dotted Line `>` Dotted Line `≤` Solid Line `≥` Solid Line First, treat the inequality sign as an equals sign and plot the curve.Graph the line `x=-1`
Since `x> -1`, we can determine that the shaded part would be the right side because all values on the right side are greater than `-1`
Next, graph the line `y=2x-1`
Use a test point to see which side of the line is to be shaded. We can try the origin, `(``0``,``0``)``y` `≤` `2``x``-1` `0` `≤` `2(``0``)-1` Substitute `(0,0)` `0` `≤` `-1` The inequality is false, so we will shade the side of the line which does not include the origin
Finally, shade the overlapping regions.