MEDAL & FAN

find the horizontal asymptote of the graph of y= -3x^6 + 5x +3 / 9x^6 + 6x + 4

Question

MEDAL & FAN

find the horizontal asymptote of the graph of y= -3x^6 + 5x +3 / 9x^6 + 6x + 4

anonymous · Answer

To solve this, we need to find the limit at infinity of the function. As x gets larger and larger, x^6 becomes so much larger than any other term that they don't matter. So we can ignore every other term and jsut look at these highest terms: -3x^6/9x^6 is -1/3.

anonymous · Answer

For example, if we had x=1,000,000, the value is -2,999,999,999,999,999,999,999,999,999,994,999,996/9,000,000,000,000,000,000,000,000,000,006,000,004 - super super super close to -1/3.

anonymous · Answer

Thank you!!

anonymous · Answer

Sure, glad to help!

anonymous · Answer

I'm not 100% sure.

Divide the coefficient of x^6 in the numerator by the same in the denominator.$$-\frac{3}{9}=-\frac{1}{3} $$

unknownrandom · Answer

@robtobey  That is correct. You do that when the Degree of the numerator=Degree of the denominator

unknownrandom · Answer

If the degree of the denominator is bigger y=0. If it is smaller There is no HA