How do you find the asymptotes for #y=(2x)/(x-3)#?

Answer 1

vertical asymptote at x = 3
horizontal asymptote at y = 2

Vertical asymptotes occur as the denominator of a rational function tends to zero. To find the equation let the denominator equal zero.

solve : x - 3 = 0 → x = 3

Horizontal asymptotes occur as #lim_(x→±∞) f(x) → 0#

If the degree of the numerator and denominator are equal the equation can be found by taking the ratio of leading coefficients. In this question they are both of degree 1.

hence : y# = 2/1 = 2 # here is the graph of the function to illustrate them. graph{2x/(x-3) [-10, 10, -5, 5]}

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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.