005 Sample Final A, Question 18 - Revision history

MathAdmin at 18:56, 2 June 2015

2015-06-02T18:56:25Z

MathAdmin at 18:50, 2 June 2015

2015-06-02T18:50:06Z

MathAdmin: Created page with "''' Question ''' Graph the following function, $f(x) = \left(\frac{1}{3}\right)^{x+1} + 1$
Make sure to label any asymptotes, and at least two..."

2015-06-01T01:36:14Z

Created page with "''' Question ''' Graph the following function, <center><math>f(x) = \left(\frac{1}{3}\right)^{x+1} + 1</math></center> <br> Make sure to label any asymptotes, and at least two..."

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''' Question ''' Graph the following function, <center><math>f(x) = \left(\frac{1}{3}\right)^{x+1} + 1</math></center> <br>
Make sure to label any asymptotes, and at least two points on the graph.

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
! Final Answers
|-
|a) False. Nothing in the definition of a geometric sequence requires the common ratio to be always positive. For example, <math>a_n = (-a)^n</math>
|-
|b) False. Linear systems only have a solution if the lines intersect. So y = x and y = x + 1 will never intersect because they are parallel.
|-
|c) False. <math>y = x^2</math> does not have an inverse.
|-
|d) True. <math>cos^2(x) - cos(x) = 0</math> has multiple solutions.
|-
|e) True.
|-
|f) False.
|}

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

@@ Line 6: / Line 6: @@
 ! Foundations
 |-
-|1) What is the basic graph of <math> f(x) = 3^{(x+1)} - 2</math>?
+|1) What is the basic graph of <math> f(x) = \left(\frac{1}{3}\right)^{x+1} + 1</math>?
 |-
-|2) How is the graph <math>g(x)=x+1</math> obtained from <math>f(x)=x</math>?
+|2) How is the graph <math>g(x)=x^3+1</math> obtained from <math>f(x)=x^3</math>?
 |-
-|3) How is the graph <math>g(x)=(x-3)^2</math> obtained from <math>f(x)=x^2</math>?
+|3) How is the graph <math>g(x)=(x+1)^2</math> obtained from <math>f(x)=x^2</math>?
 |-
 |Answer:
 |-
-|1) The basic graph is <math>y=3^x</math>.
+|1) The basic graph is <math>y=\left(\frac{1}{3}\right)^x</math>.
 |-
 |2) The graph of <math>g(x)</math> is obtained by shifting the graph of <math>f(x)</math> up 1 unit.
 |-
-|3) The graph of <math>g(x)</math> is obtained by shifting the graph of <math>f(x)</math> to the right by 3 units.
+|3) The graph of <math>g(x)</math> is obtained by shifting the graph of <math>f(x)</math> to the left by 1 unit.
 |}
@@ Line 27: / Line 27: @@
 ! Step 1:
 |-
-|We start with the basic graph of <math>g(x)=3^x</math>.
+|We start with the basic graph of <math>g(x)=\left(\frac{1}{3}\right)^x</math>.
 |-
-|To get the graph of <math>f(x)</math> from <math>g(x)</math>, we shift the graph of <math>g(x)</math> down 2 and to the left by 1.
+|To get the graph of <math>f(x)</math> from <math>g(x)</math>, we shift the graph of <math>g(x)</math> up 2 and to the left by 1.
 |}
@@ Line 35: / Line 35: @@
 ! Step 2:
 |-
-|Two ordered pairs are (-1,-1), and (0,1). There is a horizontal asymptote at <math>y=-2</math>.
+|Two ordered pairs are <math>\left(0, \frac{4}{3}\right)</math> &nbsp; and &nbsp; <math>(-1, 1)</math>. There is a horizontal asymptote at <math>y = 1</math>.
 |}
@@ Line 41: / Line 41: @@
 ! Final Answer:
 |-
-|To get the graph of <math>f(x)</math> from <math>3^x</math>, we shift the graph of <math>3^x</math> down 2 and to the left by 1.
+|To get the graph of <math>f(x)</math> from <math>\left(\frac{1}{3}\right)^x</math>, we shift the graph of <math>\left(\frac{1}{3}\right)^x</math> up 1 and to the left by 1.
 |-
+|
-[[File:4_Sample_Final_5.png]]
+[[File:5_Sample_Final_18.png]]
 |}
 [[005 Sample Final A|'''<u>Return to Sample Exam</u>''']]

@@ Line 4: / Line 4: @@
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-! Final Answers
+! Foundations
 |-
-|a) False. Nothing in the definition of a geometric sequence requires the common ratio to be always positive. For example, <math>a_n = (-a)^n</math>
+|1) What is the basic graph of <math> f(x) = 3^{(x+1)} - 2</math>?
 |-
-|b) False. Linear systems only have a solution if the lines intersect. So y = x and y = x + 1 will never intersect because they are parallel.
+|2) How is the graph <math>g(x)=x+1</math> obtained from <math>f(x)=x</math>?
 |-
-|c) False. <math>y = x^2</math> does not have an inverse.
+|3) How is the graph <math>g(x)=(x-3)^2</math> obtained from <math>f(x)=x^2</math>?
 |-
-|d) True. <math>cos^2(x) - cos(x) = 0</math> has multiple solutions.
+|Answer:
 |-
-|e) True.
+|1) The basic graph is <math>y=3^x</math>.
 |-
-|f) False.
+|2) The graph of <math>g(x)</math> is obtained by shifting the graph of <math>f(x)</math> up 1 unit.
 |}
 [[005 Sample Final A|'''<u>Return to Sample Exam</u>''']]

005 Sample Final A, Question 18 - Revision history

MathAdmin at 18:56, 2 June 2015

MathAdmin at 18:50, 2 June 2015

MathAdmin: Created page with "''' Question ''' Graph the following function, f(x) = \left(\frac{1}{3}\right)^{x+1} + 1 Make sure to label any asymptotes, and at least two..."

MathAdmin: Created page with "''' Question ''' Graph the following function, $f(x) = \left(\frac{1}{3}\right)^{x+1} + 1$
Make sure to label any asymptotes, and at least two..."