# How do you find the asymptotes for #y=(2x^2 + 3)/(x^2 - 6)#?

VA:

HA:

Vertical Asymptotes

Horizontal Asymptotes

graph{(2x^2+3)/(x^2-6) [-19.62, 20.93, -8.83, 11.45]}

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To find the asymptotes for the function (y = \frac{2x^2 + 3}{x^2 - 6}), follow these steps:

- Determine if there are any vertical asymptotes by identifying values of (x) that make the denominator zero. These values will be vertical asymptotes.
- Determine if there are any horizontal or oblique asymptotes by comparing the degrees of the numerator and denominator.
- If the degree of the numerator is less than the degree of the denominator, there is a horizontal asymptote at (y = 0).
- If the degree of the numerator is equal to the degree of the denominator, divide the numerator by the denominator to find the equation of the oblique asymptote.
- If the degree of the numerator is greater than the degree of the denominator, there are no horizontal or oblique asymptotes.
- Finally, check for any holes in the graph by simplifying the function and canceling common factors if possible.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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