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 | one billion one hundred twenty-four million sixty-six thousand one hundred forty-nine |
---|

- 1124066149 has 4 divisors, whose sum is
**1131225964** - The reverse of 1124066149 is
**9416604211** - Previous prime number is
**157**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 34
- Digital Root 7

Name | two hundred five million five hundred six thousand five hundred sixty-five |
---|

- 205506565 has 8 divisors, whose sum is
**226550016** - The reverse of 205506565 is
**565605502** - Previous prime number is
**11**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 34
- Digital Root 7

Name | one hundred sixty-nine million three hundred forty-four thousand three hundred eighty-seven |
---|

- 169344387 has 8 divisors, whose sum is
**188362800** - The reverse of 169344387 is
**783443961** - Previous prime number is
**977**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 45
- Digital Root 9