How do you find the asymptotes for #y=2/(x+1)#?
First look at what makes the denominator
in "the language" instead:
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To find the asymptotes for the function y=2/(x+1), we need to consider two types of asymptotes: vertical asymptotes and horizontal asymptotes.
Vertical asymptotes occur when the denominator of the function becomes zero. In this case, the denominator is (x+1). Setting it equal to zero, we get x+1=0, which gives us x=1. Therefore, the vertical asymptote for the given function is x=1.
Horizontal asymptotes can be determined by analyzing the behavior of the function as x approaches positive or negative infinity. In this case, as x becomes very large (positive or negative), the value of y approaches zero. Hence, the horizontal asymptote for the given function is y=0.
To summarize:
 Vertical asymptote: x=1
 Horizontal asymptote: y=0
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To find the asymptotes for the function ( y = \frac{2}{x + 1} ):

Vertical asymptote: Set the denominator equal to zero and solve for ( x ). The vertical asymptote occurs at the value(s) of ( x ) that make the denominator zero. In this case, the vertical asymptote is ( x = 1 ).

Horizontal asymptote: Examine the behavior of the function as ( x ) approaches positive or negative infinity. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is at ( y = 0 ). In this case, the degree of the numerator is less than the degree of the denominator, so the horizontal asymptote is ( y = 0 ).
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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