Answer:
the correct answer is a. The function approaches a horizontal asymptote.
Step-by-step explanation:
When the degree of the numerator is less than the degree of the denominator, the end behavior of the function is determined by the degree of the denominator.
If the degree of the denominator is greater than the degree of the numerator, the function will approach a horizontal asymptote. The horizontal asymptote is a horizontal line that the function gets closer and closer to as the input values (x-values) become larger or smaller.
For example, if we have a rational function with a degree 1 numerator and a degree 2 denominator, such as f(x) = (2x + 1) / (x^2 + 1), the degree of the denominator (2) is greater than the degree of the numerator (1). In this case, 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.
It's important to note that this answer assumes that the denominator does not have any factors that would cause vertical asymptotes or slant asymptotes. If the denominator has factors that cause vertical asymptotes or slant asymptotes, the end behavior may be different.
