Answer:
the correct answer is a. The function approaches a horizontal asymptote.
Step-by-step explanation:
The correct answer is a. The function approaches a horizontal asymptote.
When the degree of the numerator is the same as the degree of the denominator, the end behavior of the function is determined by the leading terms of the numerator and denominator. The leading term is the term with the highest power of x.
If the degree of the numerator is the same as the degree of the denominator, the leading terms will have the same degree. In this case, the end behavior of the function is determined by the coefficients of the leading terms.
For example, if we have a rational function with a degree 2 numerator and a degree 2 denominator, such as f(x) = (3x^2 - 2) / (2x^2 + 5), the degree of the numerator (2) is the same as the degree of the denominator (2). In this case, the leading terms are 3x^2 and 2x^2. Since the coefficients of the leading terms are the same (3 and 2), the function will approach a horizontal asymptote as the x-values increase or decrease.
Therefore, the correct answer is a. The function approaches a horizontal asymptote.
