004 Sample Final A, Problem 4 - Revision history

MathAdmin at 17:08, 2 June 2015

2015-06-02T17:08:44Z

MathAdmin at 17:01, 2 June 2015

2015-06-02T17:01:33Z

MathAdmin: Created page with " Graph the system of inequalities. $y > 2x - 3 \qquad y \le 4-x^2$ {| class="mw-collapsible mw-collapsed" style = "text-align:left;" ! Foundation..."

2015-06-01T05:47:12Z

Created page with "<span class="exam"> Graph the system of inequalities. <math>y > 2x - 3 \qquad y \le 4-x^2</math> {| class="mw-collapsible mw-collapsed" style = "text-align:left;" ! Foundation..."

New page

<span class="exam"> Graph the system of inequalities. <math>y > 2x - 3 \qquad y \le 4-x^2</math>
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
! Foundations
|-
|How do we graph <math>y>x</math>?
|-
|Answer:
|-
|We replace the inequality <math>></math> with <math>=</math>. Now, we have the equation of a line.
|-
|Since the sign was <math>></math> and not <math>\geq </math>, the line is dashed. Now, since <math>y>x</math>,
|-
|we shade in the area to the left of the line.
|}

Solution:

{| class = "mw-collapsible mw-collapsed" style = "text-align:left;"
! Step 1:
|-
|
|-
|
|}

{|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
! Step 2:
|-
|
|}

{|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
! Step 3:
|-
|
|-
|
|-
|
|-
|
|}

{|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
! Step 4:
|-
|
|-
|
|-
|
|}

{|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
! Final Answer:
|-
|
|}

[[004 Sample Final A|<u>'''Return to Sample Exam</u>''']]

@@ Line 5: / Line 5: @@
 ! Step 1: &nbsp;
 |-
-|First we replace the inequalities with equality. So <math>y = \vert x\vert + 1</math>, and <math>x^2 + y^2 = 9</math>.
+|First we replace the inequalities with equality. So <math>y = 2x - 3</math>, and <math>y = 4 - x^2</math>.
 |-
 |Now we graph both functions.
@@ Line 19: / Line 19: @@
 |point satisfies the inequality or not. For both equations we will pick the origin.
 |-
-|<math>y < \vert x\vert + 1:</math> Plugging in the origin we get, <math>0 < \vert 0\vert + 1 = 1</math>. Since the inequality is satisfied shade the side of
+|<math>y > 2x - 3:</math> Plugging in the origin we get, <math> 0 > 2(0) - 3 = -3 </math>. Since the inequality is false, we shade the side of
 |-
-|<math>y < \vert x\vert + 1</math> that includes the origin. We make the graph of <math>y < \vert x\vert + 1</math>, since the inequality is strict.
+|<math>y = 2x - 3</math> that does not include the origin. We make the graph of <math>y < \vert x\vert + 1</math> dashed, since the inequality is strict.
 |-
-|<math>x^2 + y^2 \le 9:</math> <math>(0)^2 +(0)^2 = 0 \le 9</math>. Once again the inequality is satisfied. So we shade the inside of the circle.
+|<math>y \le 4 - x^2:</math> Plugging in the origin we get <math>0 \le 4 - (0)^2 = 4</math>. Since this inequality is true, we shade the side of <math>y = 4 - x^2</math> that includes the origin. Here we make the graph of <math> y = 4 - x^2 </math> solid since the inequality sign is <math>\le</math>
 |}
@@ Line 31: / Line 29: @@
 ! Final Answer: &nbsp;
 |-
-|The final solution is the portion of the graph that below <math>y = \vert x\vert + 1</math> and inside <math> x^2 + y^2 = 9</math>
+|The final solution is the portion of the graph that below <math>y = 4 - x^2</math> and above <math> y = 2x - 3</math>
 |-
 |The region we are referring to is shaded both blue and red.
 |-
-|[[File:8A_Final_5.png]]
+|[[File:4_Sample_Final_4.png]]
 |}
 [[004 Sample Final A|<u>'''Return to Sample Exam</u>''']]

@@ Line 1: / Line 1: @@
 <span class="exam"> Graph the system of inequalities. <math>y > 2x - 3 \qquad y \le 4-x^2</math>
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-! Foundations
+! Step 1: &nbsp;
 |-
-|Since the sign was <math>></math> and not <math>\geq </math>, the line is dashed. Now, since <math>y>x</math>,
+|First we replace the inequalities with equality. So <math>y = \vert x\vert + 1</math>, and <math>x^2 + y^2 = 9</math>.
 |-
-|we shade in the area to the left of the line.
+|Now we graph both functions.
 |}
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-Solution:
+! Step 2: &nbsp;
 |-
+|Now that we have graphed both functions we need to know which region to shade with respect to each graph.
 |-
+|To do this we pick a point an equation and a point not on the graph of that equation. We then check if the
 |-
+|point satisfies the inequality or not. For both equations we will pick the origin.
 |-
+|<math>y < \vert x\vert + 1:</math> Plugging in the origin we get, <math>0 < \vert 0\vert + 1 = 1</math>. Since the inequality is satisfied shade the side of
 |-
+|<math>y < \vert x\vert + 1</math> that includes the origin. We make the graph of <math>y < \vert x\vert + 1</math>, since the inequality is strict.
 |-
+|<math>x^2 + y^2 \le 9:</math> <math>(0)^2 +(0)^2 = 0 \le 9</math>. Once again the inequality is satisfied. So we shade the inside of the circle.
 |-
+|We also shade the boundary of the circle since the inequality is <math>\le</math>
 |}
-{|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
+{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-! Step 4:
+! Final Answer: &nbsp;
 |-
+|The final solution is the portion of the graph that below <math>y = \vert x\vert + 1</math> and inside <math> x^2 + y^2 = 9</math>
 |-
+|The region we are referring to is shaded both blue and red.
 |-
+|[[File:8A_Final_5.png]]
 |}
 [[004 Sample Final A|<u>'''Return to Sample Exam</u>''']]

004 Sample Final A, Problem 4 - Revision history

MathAdmin at 17:08, 2 June 2015

MathAdmin at 17:01, 2 June 2015

MathAdmin: Created page with " Graph the system of inequalities. y > 2x - 3 \qquad y \le 4-x^2 {| class="mw-collapsible mw-collapsed" style = "text-align:left;" ! Foundation..."

MathAdmin: Created page with " Graph the system of inequalities. $y > 2x - 3 \qquad y \le 4-x^2$ {| class="mw-collapsible mw-collapsed" style = "text-align:left;" ! Foundation..."