Find the horizontal asymptote of the graph of y = 3x^6 - 7x + 10/ 8x^5 +9x +10
To find the horizontal asymptote of the graph of the given function, we need to examine the behavior of the function as x approaches positive or negative infinity.
As x approaches positive infinity, the term with the highest degree (x^6) in the numerator and the denominator dominates the fraction. Since the leading term of the numerator has a higher degree than the leading term of the denominator, the fraction approaches positive infinity as x approaches positive infinity.
As x approaches negative infinity, again the term with the highest degree dominates the fraction. This time, the leading term of the denominator (8x^5) has a higher degree than the leading term of the numerator. Therefore, the fraction approaches 0 as x approaches negative infinity.
Since the function approaches different values as x approaches positive and negative infinity, the graph of the function does not have a horizontal asymptote.
In summary, the graph of the given function does not have a horizontal asymptote.