Difference between revisions of "005 Sample Final A, Question 18"

Revision as of 10:50, 2 June 2015

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 points on the graph.

Foundations
1) What is the basic graph of $f(x)=3^{(x+1)}-2$ ?
2) How is the graph $g(x)=x+1$ obtained from $f(x)=x$ ?
3) How is the graph $g(x)=(x-3)^{2}$ obtained from $f(x)=x^{2}$ ?
Answer:
1) The basic graph is $y=3^{x}$ .
2) The graph of $g(x)$ is obtained by shifting the graph of $f(x)$ up 1 unit.
3) The graph of $g(x)$ is obtained by shifting the graph of $f(x)$ to the right by 3 units.

Solution:

Step 1:
We start with the basic graph of $g(x)=3^{x}$ .
To get the graph of $f(x)$ from $g(x)$ , we shift the graph of $g(x)$ down 2 and to the left by 1.

Step 2:
Two ordered pairs are (-1,-1), and (0,1). There is a horizontal asymptote at $y=-2$ .

Final Answer:
To get the graph of $f(x)$ from $3^{x}$ , we shift the graph of $3^{x}$ down 2 and to the left by 1.
Two ordered pairs are (-1,-1), and (0,1). There is a horizontal asymptote at $y=-2$

Return to Sample Exam

@@ 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.
+|-
+|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.
+|}
+Solution:
+{| class = "mw-collapsible mw-collapsed" style = "text-align:left;"
+! Step 1:
+|-
+|We start with the basic graph of <math>g(x)=3^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.
+|}
+{|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
+! Step 2:
+|-
+|Two ordered pairs are (-1,-1), and (0,1). There is a horizontal asymptote at <math>y=-2</math>.
+|}
+{|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
+! 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.
+|-
+|Two ordered pairs are (-1,-1), and (0,1). There is a horizontal asymptote at <math>y=-2</math>
+|-
+|
+[[File:4_Sample_Final_5.png]]
 |}
 [[005 Sample Final A|'''<u>Return to Sample Exam</u>''']]

Difference between revisions of "005 Sample Final A, Question 18"

Revision as of 10:50, 2 June 2015

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