Graphing rational functions

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8 Terms

1
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    2x² + 3x - 6

----------------------

        x³ + 3x   

  • what’s the horizontal asymptote?

0

2
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2x² + 3x - 6

------------------------

x² + 3

  • what’s the horizontal asymptote?

2/1

3
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    2x² + 3x - 6

------------------------

         x + 3

  • what’s the horizantal asymptote?

none - it’s oblique

  • divide numerator by denominator, and take polynomial part (end behavior) 

<p>none - it’s <strong>oblique</strong></p><ul><li><p>divide numerator by denominator, and take polynomial part (end behavior)&nbsp;</p></li></ul><p></p>
4
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. 2x² + 3x - 6

------------------------

       x³ + 3x   

  • what’s the vertical asymptote?

(set denominator to 0)

  • x=0

5
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     2x² + 3x - 6

------------------------

         x² + 3

  • what’s the horizontal asymptote?

(set denominator to 0)

  • x=none (cant take ²⟌-3)

6
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2x² + 3x - 6

------------------------

         x + 3

  • what’s the vertical asymptote?

(set denominator to 0)

  • x=-3

7
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how to find holes

when something cancels out - 0/0

  • answer form: (x, y)

8
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how to find roots

set remaining factor in the numerator to 0 after canceling - 0/#

  • answer form: x=___