Toggle navigation
Ask Questions
Ask
Answer Questions
Answer
Users
FAQ
Login
Register
Preview 50% of the Answer Below
Due to formatting, images, tables, or paragraphs may be out of place or not shown. Rest assured that they will be included and formatted correctly in your purchased answer.
Details
Question Title:
Honors Precalculus Limits problem
Go Back to the Question
Answer Preview
http://m.XXXXXXXXXXXX.XXX/input/?i=+%5Bx%XXX-5x%2B4%5D%XX%XXX%5E2-1%XX+XXXX+-XX&XX;x&XX;10&x=11&y=11</a><br></p> <p>XXXX XXX vertical XXXX line is marking XXX asymptote XXX is XXX part of the function.</p> <p><XX></p> <p>Edit X:</p> <p>To graph XXXX by hand, you XXXXX XXXX to first XXXX XXX XXXXX</p> <p>XXXX you XXXX XXX XXXXX shape XX XXX graph (XXXX is XX XXX XXXX XXXXX XX a vertical XXXXXXXXX at -X and a horizontal asymptot at 1</p> <p>XXXX you would compare it XX XXXXX functions, Here this XXXXX most likely look XXXXXXX XX XXXXXXXXX like 1/x</p> <p>Finally, check XXX behavior XX either XXXX XX the asymptote</p> <p>As XX XXXX from XXX XXXX (values XXXXX -X, like -1.XX XX XX discussed above) XXX function XX going XX XX positive because the numerator, x-4 XX XXXXX XX be negative, and XXX denominator, x+1 XX XXXX XXXXX XX XX negatuve</p> <p>XXXX is to say x-4 where x&XX;4 XX XXXXXXXX</p> <p>XXX x+X where x<-X XX XXXXXXXX</p> <p>so x-X / x+1 &XX;-X XX positive</p> <p><br></p> <p>for behavior to XXX XXXXX:</p> <p>XX XXXX XXXX XXXX XXXXX XXXX -1 to X XXX XXXXXXXX is XXXXX negative</p> <p>and XX x=4, the function XX X</p> <p>because x-4 at x=4 XX X</p> <p>and x-X is non-zero</p> <p>so the XXXXXXXX XX defined, and XXXX</p> <p>So XXX function XXXX cross XXXX XXXXXXXX y values to positive y XXXXXX XX x=X</p> <p>XXX XXX both segments, the shape XXXX XX similar to X/x (XXXX is to XXX, a XXXXXXX XXXXX)</p> <p><br></p><p><br></p><p>XXXX X:</p><p>To XXXX XXXXXX you would just XXXX a small table, in the region XX interest</p><p>(x-X)/(x+1)<XX></p><p>so XXXX -10 to 10 you XXXXX XXXXXXXXX XXXX XXXXX(XXXX is the XXXX XXXXXX one)</p><table> <tbody><tr> <td>x</td> <td>y</td> </tr> <tr> <td>-XX</td> <td>X.XXXXXXXXX</td> </tr> <tr> <td>-9</td> <td>X.625</td> </tr> <tr> <td>-8</td> <td>1.714285714</td> </tr> <tr> <td>-X</td> <td>1.XXXXXXXXX</td> </tr> <tr> <td>-6</td> <td>2</td> </tr> <tr> <td>-X</td> <td>X.XX</td> </tr> <tr> <td>-X</td> <td>2.666666667</td> </tr> <tr> <td>-X</td> <td>3.X</td> </tr> <tr> <td>-X</td> <td>X</td> </tr> <tr> <td>-X</td> <td>#XXX/X!</td> </tr> <tr> <td>0</td> <td>-4</td> </tr> <tr> <td>1</td> <td>-1.X</td> </tr> <tr> <td>2</td> <td>-X.666666667</td> </tr> <tr> <td>X</td> <td>-X.25</td> </tr> <tr> <td>4</td> <td>0</td> </tr> <tr> <td>5</td> <td>0.XXXXXXXXX</td> </tr> <tr> <td>6</td> <td>X.285714286</td> </tr> <tr> <td>7</td> <td>0.XXX</td> </tr> <tr> <td>8</td> <td>X.444444444</td> </tr> <tr> <td>9</td> <td>X.5</td> </tr> <tr> <td>10</td> <td>0.545454545</td> </tr></tbody></table><p><br></p> <p>Noting that XX x = -1 is XXX vertical symptom</p><p><XX></p><p>XX, XX XXXXX XXXXXX, you know XXXX it XXXXX like XXXXXXX (XXXX X/x)</p><p>but shifted XXXX XXXX XX x=4 there is XXX y=0</p><p>and XXXX the XXXXXXXX asymptote is at -1 (XXXXXXX x=-1 XXXXXXX in dividing by zero, so no such XXXXX XXXXXX)</p><p>and XXX horizontal asymptote, because it is a ratio XX X XXXXX order polynomials, is the ratio of their co-efficients (x-X)/(x+1) where it XX XX / XX in XXXX case, so XXX horizontal asymptote XX XX y=1</p><p>So you XXX XXXX a XXXXX XXXXX y=1 XX XXX XXXXXXXXX XXXXXXX, and x=-1 XX the XXXXXXXX portion</p><p>and the XXXXXXXX will XX XX XXX top XXXX, and XXXXXX XXXXX quadrants, XXXX a shape like XXXX of 1/x</p>">
Attachment #1 Preview
