Spring 2018: the following problems are not related. (a)(10pts) suppose f (x) = x and g(x) = 4 x2. Find (g f )(x) and express the domain of this function in interval notation. (b)(10pts) suppose we know that q(x) = x3 + sin(x) + xp(x) is an odd function. Justify your answer. function p(x) the is an even function. Solution: (a)(10pts) proceeding by de nition, we have that (g f )(x) = g(f (x)) = g( x) Show all work, explain your answer. (b)(12pts) suppose that f (x) = , use limits to nd all horizontal and vertical asymptotes of f (x). = + no asymptote in this direction and lim x f (x) = lim x . = 4 h. a. at y = 4 and for the vertical asymptote, note that we just need to check the limit as x 0+, we have lim x 0+ f (x) = lim x 0+ x +
