How do you find all the asymptotes for function #f(x) = (13x) / (x+34)#?
Vertical asymptote:
Horizontal asymptote:
- Horizontal asymptote
- The oblique asymptote doesn't exist, because we have a horizontal asymptote
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To find the asymptotes for the function f(x) = (13x) / (x+34), you need to examine both vertical and horizontal asymptotes.
Vertical asymptotes occur where the denominator of the function equals zero. Set the denominator, x + 34, equal to zero and solve for x:
x + 34 = 0 x = -34
Therefore, the function has a vertical asymptote at x = -34.
Horizontal asymptotes can be found by examining the behavior of the function as x approaches positive or negative infinity. To do this, compare the degrees of the numerator and denominator of the function. In this case, the degree of the numerator (1) is less than the degree of the denominator (1). Therefore, the horizontal asymptote can be found by dividing the leading coefficients of the numerator and denominator:
Horizontal asymptote = coefficient of x in numerator / coefficient of x in denominator = 13 / 1 = 13
Thus, the function f(x) = (13x) / (x+34) has a horizontal asymptote at y = 13.
In summary, the function has one vertical asymptote at x = -34 and one horizontal asymptote at y = 13.
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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.
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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