How do you find the horizontal asymptote of the graph of #y=6x^2# ?

Answer 1

Aurora Alvarado

See explanation.

To find if a function has a horizontal assymptote you have to calculate the limit:

If the above limit is finite and equal to #a#, then the line #y=a# is a horizontal assymptote of #f(x)#.

For the function #f(x)=6x^2# both limits are equal to #+oo#, so the function does not have the horizontal asymptote.

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Answer 2

Luke Alvarez

To find the horizontal asymptote of the graph of y=6x^2, we need to determine 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=6x^2 also becomes very large. Therefore, there is no horizontal asymptote for the graph of y=6x^2.

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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.