Final answer:
A rational function is a function that can be expressed as the quotient of two polynomials, with the key features being the horizontal and vertical asymptotes. The easiest key feature to find in a rational function is the horizontal asymptote, while the most difficult key feature to find is the vertical asymptote.
Step-by-step explanation:
A rational function is a function that can be expressed as the quotient of two polynomials, where the denominator is not equal to zero. The key feature of a rational function is the presence of a fraction in the function, with the numerator and denominator being polynomials. The easiest key feature to find in a rational function is the horizontal asymptote. This is because the horizontal asymptote can be determined by looking at the degrees of the numerator and denominator polynomials. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is at y = 0. If the degree of the numerator is equal to the degree of the denominator, the horizontal asymptote is at y = the ratio of the leading coefficients of the numerator and denominator polynomials. If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote.
The most difficult key feature to find in a rational function is the vertical asymptote. To find the vertical asymptote, you need to set the denominator polynomial equal to zero and solve for x. The solutions to this equation are the x-values at which the rational function has vertical asymptotes. However, finding the solutions to this equation can be challenging depending on the complexity of the denominator polynomial.