How do you find the vertical, horizontal or slant asymptotes for #y=4/(x+4 ) #?
vertical asymptote x= -4
horizontal asymptote y = 0
Vertical asymptotes occur as the denominator of a rational function tends to zero. To find the equation let the denominator equal zero.
solve: x + 4 = 0 → x = -4 is the equation.
If the degree of the numerator is less than the degree of the denominator, as in this case , numerator degree 0, denominator degree 1 then the equation is always y = 0.
Here is the graph of the function as an illustration. graph{4/(x+4) [-10, 10, -5, 5]}
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To find the vertical asymptote of (y = \frac{4}{x+4}), set the denominator equal to zero and solve for (x). In this case, (x + 4 = 0) gives (x = -4). Therefore, there is a vertical asymptote at (x = -4).
To find the horizontal asymptote, observe the behavior of the function as (x) approaches positive or negative infinity. As (x) becomes very large (positive or negative), the term (4/(x+4)) approaches zero since the denominator becomes much larger than the numerator. Therefore, the horizontal asymptote is (y = 0).
Since the degree of the numerator is less than the degree of the denominator, there is no slant (oblique) asymptote for this function.
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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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