Difference between revisions of "004 Sample Final A, Problem 9"

From Grad Wiki
Jump to navigation Jump to search
Line 3: Line 3:
 
! Foundations
 
! Foundations
 
|-
 
|-
|  
+
|
 
|-
 
|-
 
|Answer:
 
|Answer:
Line 16: Line 16:
 
! Step 1:
 
! Step 1:
 
|-
 
|-
|
+
|Since <math>y=\frac{6}{(x-2)(x+1)}</math>, the vertical asymptotes are <math>x=2</math> and <math>x=-1</math>.
|-
 
|
 
 
|}
 
|}
  
Line 24: Line 22:
 
! Step 2:
 
! Step 2:
 
|-
 
|-
|
+
|The horizontal asymptote is <math>y=0</math>.
 
|}
 
|}
  
Line 30: Line 28:
 
! Step 3:
 
! Step 3:
 
|-
 
|-
|
+
|There is no <math>x</math> intercept since <math>y\neq 0 </math> for any <math>x</math>.
 
|-
 
|-
|
+
|Plugging in <math>x=0</math>, we get <math>y=-3</math>. So, the <math>y</math> intercept is (0,3)
|-
 
|
 
|-
 
|
 
 
|}
 
|}
  
Line 52: Line 46:
 
! Final Answer:
 
! Final Answer:
 
|-
 
|-
|
+
| The vertical asymptotes are <math>x=2</math> and <math>x=-1</math>. The horizontal asymptote is <math>y=0</math>. There is no <math>x</math> intercept and the <math>y</math> intercept is (0,3).
 
|}
 
|}
  
 
[[004 Sample Final A|<u>'''Return to Sample Exam</u>''']]
 
[[004 Sample Final A|<u>'''Return to Sample Exam</u>''']]

Revision as of 11:12, 6 May 2015

Graph the function. Give equations of any asymptotes, and list any intercepts.     

Foundations
Answer:


Solution:

Step 1:
Since , the vertical asymptotes are and .
Step 2:
The horizontal asymptote is Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y=0} .
Step 3:
There is no Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x} intercept since Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y\neq 0 } for any Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x} .
Plugging in Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x=0} , we get Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y=-3} . So, the Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y} intercept is (0,3)
Step 4:
Final Answer:
The vertical asymptotes are Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x=2} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x=-1} . The horizontal asymptote is Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y=0} . There is no Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x} intercept and the Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y} intercept is (0,3).

Return to Sample Exam