Question
Find the equation of the horizontal asymptote of the function f(x)=x^3+1/5x^2-3x^3.
y = 5/3
y = -1/3
y = 0
y = 1/5
y = 5/3
y = -1/3
y = 0
y = 1/5
Answers
GPT 3.5
The equation of the horizontal asymptote can be found by examining the behavior of the function as x approaches positive or negative infinity.
In this case, as x approaches positive infinity, the highest power of x in the function is x^3. Therefore, the function grows without bound as x approaches positive infinity. As x approaches negative infinity, the highest power of x in the function is -3x^3. Therefore, the function also grows without bound as x approaches negative infinity.
Since the function grows without bound in both directions, there is no horizontal asymptote. Therefore, the correct answer is y = 0.
In this case, as x approaches positive infinity, the highest power of x in the function is x^3. Therefore, the function grows without bound as x approaches positive infinity. As x approaches negative infinity, the highest power of x in the function is -3x^3. Therefore, the function also grows without bound as x approaches negative infinity.
Since the function grows without bound in both directions, there is no horizontal asymptote. Therefore, the correct answer is y = 0.