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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{| class="mw-collapsible mw-collapsed" style = "text-align:left;" | {| class="mw-collapsible mw-collapsed" style = "text-align:left;" | ||
− | ! | + | ! Foundations |
|- | |- | ||
− | | | + | |1) What is the basic graph of <math> f(x) = 3^{(x+1)} - 2</math>? |
|- | |- | ||
− | | | + | |2) How is the graph <math>g(x)=x+1</math> obtained from <math>f(x)=x</math>? |
|- | |- | ||
− | | | + | |3) How is the graph <math>g(x)=(x-3)^2</math> obtained from <math>f(x)=x^2</math>? |
|- | |- | ||
− | | | + | |Answer: |
|- | |- | ||
− | | | + | |1) The basic graph is <math>y=3^x</math>. |
|- | |- | ||
− | |f) | + | |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>''']] | [[005 Sample Final A|'''<u>Return to Sample Exam</u>''']] |
Revision as of 10:50, 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 right by 3 units. |
Solution:
Step 1: |
---|
We start with the basic graph of . |
To get the graph of from , we shift the graph of 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 . |
Final Answer: |
---|
To get the graph of from , we shift the graph of down 2 and to the left by 1. |
Two ordered pairs are (-1,-1), and (0,1). There is a horizontal asymptote at |