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

Revision as of 12:12, 6 May 2015

Graph the function. Give equations of any asymptotes, and list any intercepts. $y={\frac {6}{x^{2}-x-2}}$

Solution:

Step 1:
Since $y={\frac {6}{(x-2)(x+1)}}$ , the vertical asymptotes are $x=2$ and $x=-1$ .

Step 2:
The horizontal asymptote is $y=0$ .

Step 3:
There is no $x$ intercept since $y\neq 0$ for any $x$ .
Plugging in $x=0$ , we get $y=-3$ . So, the $y$ intercept is (0,3)

Final Answer:
The vertical asymptotes are $x=2$ and $x=-1$ . The horizontal asymptote is $y=0$ . There is no $x$ intercept and the $y$ intercept is (0,3).

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 ! Foundations
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 |Answer:
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 ! Step 1:
 |-
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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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 ! Step 2:
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+|The horizontal asymptote is <math>y=0</math>.
 |}
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 ! Step 3:
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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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-|-
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 |}
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 ! 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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