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

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(Created page with "<span class="exam"> Graph the function. Give equations of any asymptotes, and list any intercepts.     <math>y = \frac{6}{x^2 - x - 2}</math>")
 
 
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<span class="exam"> Graph the function. Give equations of any asymptotes, and list any intercepts. &nbsp;&nbsp;&nbsp;&nbsp;<math>y = \frac{6}{x^2 - x - 2}</math>
 
<span class="exam"> Graph the function. Give equations of any asymptotes, and list any intercepts. &nbsp;&nbsp;&nbsp;&nbsp;<math>y = \frac{6}{x^2 - x - 2}</math>
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{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
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! Foundations
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|-
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|What are the vertical asymptotes of <math>f(x)</math>?
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|-
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|Answer:
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|-
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|The vertical asymptotes are <math>x=a</math> where <math>f(a)</math> is undefined.
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|}
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Solution:
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{| class = "mw-collapsible mw-collapsed" style = "text-align:left;"
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! Step 1:
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|-
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|Since <math>y=\frac{6}{(x-2)(x+1)}</math>, the vertical asymptotes are <math>x=2</math> and <math>x=-1</math>.
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|}
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{|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
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! Step 2:
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|-
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|The horizontal asymptote is <math>y=0</math>.
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|}
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{|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
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! Step 3:
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|-
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|There is no <math>x</math> intercept since <math>y\neq 0 </math> for any <math>x</math>.
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|-
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|Plugging in <math>x=0</math>, we get <math>y=-3</math>. So, the <math>y</math> intercept is (0,3)
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|}
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{|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
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! Final Answer:
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|-
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| 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).
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|}
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[[004 Sample Final A|<u>'''Return to Sample Exam</u>''']]

Latest revision as of 13:16, 11 May 2015

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

Foundations
What are the vertical asymptotes of ?
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=a} where 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 f(a)} is undefined.


Solution:

Step 1:
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=\frac{6}{(x-2)(x+1)}} , 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} .
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)
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).

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