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 | six hundred thirty-three million nine hundred seventy-five thousand eight hundred twenty-nine |
---|

- 633975829 has 8 divisors, whose sum is
**642462912** - The reverse of 633975829 is
**928579336** - Previous prime number is
**823**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 52
- Digital Root 7

Name | two hundred seventy-seven million nine hundred eighty-six thousand five hundred fifty-seven |
---|

- 277986557 has 8 divisors, whose sum is
**281187840** - The reverse of 277986557 is
**755689772** - Previous prime number is
**8929**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 56
- Digital Root 2

Name | seven hundred forty-five million three hundred seventy thousand fifty-eight |
---|

- 745370058 has 32 divisors, whose sum is
**1522302336** - The reverse of 745370058 is
**850073547** - Previous prime number is
**487**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 39
- Digital Root 3