How do you identify the vertical asymptotes of #f(x) = (x+6)/(x^2-9x+18)#?

Answer 1

I found:
#x=6#
#x=3#

You identify the vertical asymptotes by setting the denominator equal to zero: this allows you to see which #x# values the function cannot accept (they would make the denominator equal to zero).
So, set the denominator equal to zero:
#x^2-9x+18=0# solve using the Quadratic Formula:
#x_(1,2)=(9+-sqrt(81-72))/2=(9+-3)2# so you get:
#x_1=6#
#x_2=3#
So your function cannot accept these values for #x#;
The two vertical lines of equations:
#x=6#
#x=3#
will be your "forbidden" lines or vertical asymptotes.

Graphically:

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Answer 2

To identify the vertical asymptotes of the function ( f(x) = \frac{x+6}{x^2 - 9x + 18} ), you need to find the values of ( x ) that make the denominator equal to zero. These values are the roots of the denominator polynomial. Then, any ( x )-value that makes the denominator zero but not the numerator will create a vertical asymptote. To find the roots of the denominator polynomial ( x^2 - 9x + 18 ), you can use factoring, the quadratic formula, or completing the square. Once you find the roots, those values will be the ( x )-coordinates of the vertical asymptotes.

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Answer from HIX Tutor

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.

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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