To find the horizontal asymptote of the given function y = -2^6+5x+8 / 8x^6+x+5, we first need to determine the degree of the numerator and denominator.
The degree of the numerator is determined by the highest power of x present in the numerator, which is 1 (from the term 5x). The degree of the denominator is determined by the highest power of x present in the denominator, which is 6 (from the term 8x^6).
Since the degree of the denominator is higher than the degree of the numerator, we can determine the horizontal asymptote by dividing the leading coefficients of the numerator and denominator.
In this case, the horizontal asymptote is y = 0 (option b) because the leading coefficient of the numerator is 5 and the leading coefficient of the denominator is 8. Therefore, the horizontal asymptote is y = 0.
Find the horizontal asymptote of the graph of y = -2^6+5x+8/8x^6+x+5
a. y = 1/4
b. y = 0
c. y = 1
d. no horizontal asymptote
1 answer
1 answer