Divide each term in <math><mstyle displaystyle="true"><mi>x</mi><mi>y</mi><mo>=</mo><mo>-</mo><mn>8</mn></mstyle></math> by <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

Cancel the common factor.

Divide <math><mstyle displaystyle="true"><mi>y</mi></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Move the negative in front of the fraction.

Find where the expression <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>8</mn></mrow><mrow><mi>x</mi></mrow></mfrac></mstyle></math> is undefined.

Consider the rational function <math><mstyle displaystyle="true"><mi>R</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mfrac><mrow><mi>a</mi><msup><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></msup></mrow><mrow><mi>b</mi><msup><mrow><mi>x</mi></mrow><mrow><mi>m</mi></mrow></msup></mrow></mfrac></mstyle></math> where <math><mstyle displaystyle="true"><mi>n</mi></mstyle></math> is the degree of the numerator and <math><mstyle displaystyle="true"><mi>m</mi></mstyle></math> is the degree of the denominator.

1. If <math><mstyle displaystyle="true"><mi>n</mi><mo><</mo><mi>m</mi></mstyle></math> , then the x-axis, <math><mstyle displaystyle="true"><mi>y</mi><mo>=</mo><mn>0</mn></mstyle></math> , is the horizontal asymptote.

2. If <math><mstyle displaystyle="true"><mi>n</mi><mo>=</mo><mi>m</mi></mstyle></math> , then the horizontal asymptote is the line <math><mstyle displaystyle="true"><mi>y</mi><mo>=</mo><mfrac><mrow><mi>a</mi></mrow><mrow><mi>b</mi></mrow></mfrac></mstyle></math> .

3. If <math><mstyle displaystyle="true"><mi>n</mi><mo>></mo><mi>m</mi></mstyle></math> , then there is no horizontal asymptote (there is an oblique asymptote).

Find <math><mstyle displaystyle="true"><mi>n</mi></mstyle></math> and <math><mstyle displaystyle="true"><mi>m</mi></mstyle></math> .

Since <math><mstyle displaystyle="true"><mi>n</mi><mo><</mo><mi>m</mi></mstyle></math> , the x-axis, <math><mstyle displaystyle="true"><mi>y</mi><mo>=</mo><mn>0</mn></mstyle></math> , is the horizontal asymptote.

There is no oblique asymptote because the degree of the numerator is less than or equal to the degree of the denominator.

No Oblique Asymptotes

This is the set of all asymptotes.

Vertical Asymptotes: <math><mstyle displaystyle="true"><mi>x</mi><mo>=</mo><mn>0</mn></mstyle></math>

Horizontal Asymptotes: <math><mstyle displaystyle="true"><mi>y</mi><mo>=</mo><mn>0</mn></mstyle></math>

No Oblique Asymptotes

Vertical Asymptotes: <math><mstyle displaystyle="true"><mi>x</mi><mo>=</mo><mn>0</mn></mstyle></math>

Horizontal Asymptotes: <math><mstyle displaystyle="true"><mi>y</mi><mo>=</mo><mn>0</mn></mstyle></math>

No Oblique Asymptotes

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Name | two billion eighty-six million six hundred sixty-five thousand five hundred eighty-nine |
---|

- 2086665589 has 4 divisors, whose sum is
**2105809420** - The reverse of 2086665589 is
**9855666802** - Previous prime number is
**109**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 55
- Digital Root 1

Name | one billion nine hundred forty-seven million nine hundred nineteen thousand five hundred fourteen |
---|

- 1947919514 has 8 divisors, whose sum is
**2923449888** - The reverse of 1947919514 is
**4159197491** - Previous prime number is
**1867**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 50
- Digital Root 5

Name | one hundred thirty-four million three hundred ninety-four thousand six hundred eighty |
---|

- 134394680 has 128 divisors, whose sum is
**624024000** - The reverse of 134394680 is
**086493431** - Previous prime number is
**449**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 38
- Digital Root 2