Question

Which of the following functions has the same end behavior as the rational function r given by r(x) = (x² - 5x + 3) / 2x + 6 ?

a. f(x) = 1/2
b. g(x) = x
c. h(x) = -x
d. k(x) = x²

Answer 1

The function that has the same end behavior as the given rational function r(x) = (x² - 5x + 3) / (2x + 6) is d. k(x) = x².

Step-by-step explanation:

The end behavior of a rational function is determined by the degree of the numerator and the denominator. In this case, the degree of the numerator is 2 and the degree of the denominator is 1. Since the degree of the numerator is greater than the degree of the denominator, the end behavior of the function will approach positive infinity as x approaches positive or negative infinity.

So, the function that has the same end behavior as the given rational function r(x) = (x² - 5x + 3) / (2x + 6) is d. k(x) = x².