What is the equation of the horizontal asymptote for the function?
f(x)=7x^4−18x/2x^4+14x^3
A. y=7/2
B. y=-9/7
C. y=-1/2
D. y=0
To find the equation of the horizontal asymptote of the function f(x), we need to determine the behavior of the function as x approaches positive or negative infinity.
First, let's consider the highest power of x in the numerator and denominator, which is x^4. As x approaches positive or negative infinity, the lower powers of x become insignificant compared to x^4.
Therefore, we can simplify the function by dividing the coefficients of x^4 in the numerator and denominator:
f(x) = (7x^4 - 18x) / (2x^4 + 14x^3)
≈ (7x^4) / (2x^4)
≈ 7/2
As x approaches positive or negative infinity, the function f(x) approaches 7/2.
Therefore, the equation of the horizontal asymptote is: y = 7/2. Answer choice A is correct.