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

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(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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! Final Answers
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! Foundations
 
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|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>
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|1) What is the basic graph of <math> f(x) = \left(\frac{1}{3}\right)^{x+1} + 1</math>?
 
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|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.
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|2) How is the graph <math>g(x)=x^3+1</math> obtained from <math>f(x)=x^3</math>?
 
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|c) False. <math>y = x^2</math> does not have an inverse.
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|3) How is the graph <math>g(x)=(x+1)^2</math> obtained from <math>f(x)=x^2</math>?
 
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|d) True. <math>cos^2(x) - cos(x) = 0</math> has multiple solutions.
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|Answer:
 
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|e) True.
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|1) The basic graph is <math>y=\left(\frac{1}{3}\right)^x</math>.
 
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|f) False.  
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|2) The graph of <math>g(x)</math> is obtained by shifting the graph of <math>f(x)</math> up 1 unit.
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|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.
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Solution:
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! Step 1:
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|We start with the basic graph of <math>g(x)=\left(\frac{1}{3}\right)^x</math>.
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|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.
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! Step 2:
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|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>.
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! Final Answer:
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|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.
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[[File:5_Sample_Final_18.png]]
 
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[[005 Sample Final A|'''<u>Return to Sample Exam</u>''']]
 
[[005 Sample Final A|'''<u>Return to Sample Exam</u>''']]

Latest revision as of 10:56, 2 June 2015

Question Graph the following function,


Make sure to label any asymptotes, and at least two points on the graph.


Foundations
1) What is the basic graph of ?
2) How is the graph obtained from ?
3) How is the graph obtained from ?
Answer:
1) The basic graph is .
2) The graph of is obtained by shifting the graph of up 1 unit.
3) The graph of is obtained by shifting the graph of to the left by 1 unit.


Solution:

Step 1:
We start with the basic graph of .
To get the graph of from , we shift the graph of up 2 and to the left by 1.
Step 2:
Two ordered pairs are   and   . There is a horizontal asymptote at .
Final Answer:
To get the graph of from , we shift the graph of up 1 and to the left by 1.

5 Sample Final 18.png

Return to Sample Exam

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