COLLEGE ALGEBRA (MA124) - 3.5 HOMEWORK 2023 COMPLETE QUESTIONS AND ANSWERS ALREADY PASSED A+

All rational functions can be expressed as f(x)=p(x)/q(x), where p and q are _______________ functions and q(x)=0 - CORRECT ANS polynomial The domain of every rational function is the set of all real numbers. - CORRECT ANS false The graph of the reciprocal function f(x)= 1/x has a break and is composed of two distinct branches. - CORRECT ANS true If the graph of a function f increases or decreases without bound as x approaches a, then the line x=a is __________________- of the graph of f. The equation of such a line for the graph of f(x)= 6/x+2 is _______. - CORRECT ANS - a vertical asymptote - x=-2 If the graph of a function f approaches b as x increases or decreases without bound, then the line y=b is _________________ of the graph of f. The equation of such a line for the graph of y= x-10/3x^2+1+1 is __________. The equation of such a line for the graph of y= x^2-10/ 3x^2+x+1 is ____________. - CORRECT ANS - a horizontal asymptote - y=0 - y=1/3 If the degree of the numerator of a rational function equals the degree of the denominator, then the ratio of the leading coefficients gives rise to the horizontal asymptote. - CORRECT ANS true Compared to the graph of f(x) = 1/x, the graph of g(x)= 1/x+4 -6 is shifted 4 unit(s) ___________ and 6 unit(s) _________. - CORRECT ANS - left - down The graph of a rational function has a slant asymptote if the degree of the numerator is _______ the degree of the denominator. - CORRECT ANS one more than Based on the synthe