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

From Math Wiki
Jump to navigation Jump to search
 
Line 6: Line 6:
 
! Foundations
 
! 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:
 
|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.  
 
|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:
 
! 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:
 
! 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:
 
! 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.
|-
 
|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]]
+
[[File:5_Sample_Final_18.png]]
 
|}
 
|}
  
 
[[005 Sample Final A|'''<u>Return to Sample Exam</u>''']]
 
[[005 Sample Final A|'''<u>Return to Sample Exam</u>''']]

Latest revision as of 11:56, 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