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

Latest revision as of 14:16, 11 May 2015

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

Foundations
What are the vertical asymptotes of $f(x)$ ?
Answer:
The vertical asymptotes are $x=a$ where $f(a)$ is undefined.

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).

@@ Line 1: / Line 1: @@
 <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>
+{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
+! Foundations
+|-
+|What are the vertical asymptotes of <math>f(x)</math>?
+|-
+|Answer:
+|-
+|The vertical asymptotes are <math>x=a</math> where <math>f(a)</math> is undefined.
+|}
+Solution:
+{| class = "mw-collapsible mw-collapsed" style = "text-align:left;"
+! 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>.
+|}
+{|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
+! Step 2:
+|-
+|The horizontal asymptote is <math>y=0</math>.
+|}
+{|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
+! 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)
+|}
+{|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
+! 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>''']]