How do you find the asymptotes for # f(x)=x/(x-7)#?

Answer 1

vertical asymptote x = 7 , horizontal asymptote y = 1

Find vertical asymptotes when denominator of a

rational function is zero.

so equate : x - 7 = 0 → x = 7

If the degree of the numerator and the degree of the

denominator are equal a horizontal asymptote exists.

Here they are both of degree 1 and so equal.

To obtain equation take the ratio of coefficients of leading terms.

hence # y = 1/1 rArr y = 1 #

The graph illustrates these.

graph{x/(x-7) [-10, 10, -5, 5]}

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Answer 2

To find the asymptotes of ( f(x) = \frac{x}{x - 7} ), we identify the vertical and horizontal asymptotes:

  1. Vertical asymptote: Set the denominator equal to zero and solve for ( x ): ( x - 7 = 0 ) ( x = 7 ) Therefore, there is a vertical asymptote at ( x = 7 ).

  2. Horizontal asymptote: If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is at ( y = 0 ). So, the horizontal asymptote for ( f(x) = \frac{x}{x - 7} ) is ( y = 1 ).

Therefore, the vertical asymptote is ( x = 7 ) and the horizontal asymptote is ( y = 1 ).

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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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