SOLUTION: I am not understanding the vertical and horizontal asympote of the rational function. Can someone please help me? Find the vertical asympote of the rational function f(x)= 3x-12

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Question 45304: I am not understanding the vertical and horizontal asympote of the rational function. Can someone please help me?
Find the vertical asympote of the rational function f(x)= 3x-12/4x-2
Find the horizontal asympote of the rational function f(x)= 8x-12/4x-2
Any help and explanation would be greatly apprecaited.
Thank you
Answer by jake_6233(74) (Show Source):
You can put this solution on YOUR website!
Find the vertical asympote of the rational function f(x)= 3x-12/4x-2
Find the horizontal asympote of the rational function f(x)= 8x-12/4x-2
by definition a vertical asymptote f(x) goes to infinity or negative infinity so the vetical asymptote is x =1/2 this is because if you plug x=1/2 into the denominator you will get 0
By definition a horizontal asymptote is defined f(x)=b as x goes to positive or negative infinity so (8x-12)/(4x-2) we have y=2 this is because as x gets very large or very small you will get closer and closer to 8/4 or 2 realixe that the -12 and -2 are constants that "drop out" a "trick" is to use the coeficcients of x as long as x has the same power in both the numerator and denominator
Please let me know if this helps you