Difference between revisions of "004 Sample Final A, Problem 9"
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! Foundations | ! Foundations | ||
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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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| − | | | + | |The horizontal asymptote is <math>y=0</math>. |
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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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| − | | | + | |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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! Final Answer: | ! Final Answer: | ||
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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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[[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 |
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| Answer: |
Solution:
| Step 1: |
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| Since , the vertical asymptotes are and . |
| Step 2: |
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| 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: |
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| 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) |
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| Final Answer: |
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| 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). |