Consider the rational function F(x)= (2x-3)(x^ 2 +1)(x+4) (x-5)(-3x^ 2 +2)

MATHEMATICS · Subjective · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions

Problem

Consider the rational function F(x)=(2x−3)(x2+1)(x+4)(x−5)(−3x2+2).F(x)=\frac{(2x-3)(x^{2}+1)(x+4)}{(x-5)(-3x^{2}+2)}. (a) Determine the degree of the numerator and the degree of the denominator. (b) Find lim⁡x→∞F(x)\displaystyle \lim_{x\to\infty} F(x), showing all necessary steps. (c) Find lim⁡x→−∞F(x)\displaystyle \lim_{x\to -\infty} F(x) and explain carefully how the signs of the leading terms influence the result. (d) Using your answers to parts (b) and (c), state the equation(s) of any horizontal asymptote(s) of the graph of y=F(x)y=F(x).

Related theory

Browse the problem library