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How do you find vertical, horizontal and oblique asymptotes for #y =(3/x)+2#?

Answer 1

Sophie Adams

Vertical asymptote: #x = 0#
Horizontal asymptote: #y = 2#
Oblique asymptote: none

Find a common denominator for the function: #y = 3/x +(2x)/x = (3+2x)/x = (2x+3)/x#

Rational Function: #(N(x))/(D(x))#, when #N(x) = 0# gives x-intercepts, when #D(x) = 0# you find vertical asymptotes.

Vertical asymptote at # x = 0#

When #(N(x))/(D(x)) =( a_nx^n+....)/(b_mx^m+....)# where #n, m# are the degrees of the polynomials.

If #n=m# horizontal asymptote is at #y=a_n/b_m#

#n = m = 1#, so Horizontal asymptote: #y = 2/1; y = 2#

To have an oblique or slant asymptote, #m+1 = n# which is not the case, so there is no oblique asymptote.

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Answer 2

Theodore Amidon

Vertical asymptote: ( x = 0 )

Horizontal asymptote: ( y = 0 )

Oblique asymptote: None

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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.