Find the horizontal asymptote of the graph of y = -2x^6 5x 8/ 8x^6+ 6x+5
a) y=-1/4
b) y=0
c) y=1
d) no horizontal asymptote
To find the horizontal asymptote of the graph of the given function, we need to analyze the behavior of the function as x approaches positive or negative infinity.
As x approaches positive or negative infinity, the highest power term in the numerator and denominator (x^6) dominates the function.
Since the highest power term is the same in the numerator and denominator, we can compare their coefficients to determine the horizontal asymptote.
The coefficient of x^6 in the numerator is -2, and the coefficient of x^6 in the denominator is 8.
Therefore, as x approaches positive or negative infinity, the function approaches -2/8 = -1/4.
Hence, the horizontal asymptote of the graph of the given function is y = -1/4.
Therefore, the correct option is:
a) y = -1/4.