3.10 Homework 1. The rational function r is given by r(a) = date. For what values of a does r(x) = 0? (A) = -2.303 and x = 1.000 only (B) = -1.643 and r = 1.144 only (C) = = -2.303, x = 1.000, and x = 1.303 only (D) = = -2.303, x = -1.643, x = 1.000, x = 1.303, and x = 1.144 2. The rational function r is given by r(a) = a tax tax . On what intervals of a is r(x) 2 0? (A) x20 (B) -3 3 only (D) -3 > 3 3. The rational function f is given by f(x) = (x 1)(2+3) 25+2x-5 , where k is a positive integer. For which of the following values of k will the graph of f have a horizontal asymptote at y = 0 ? (A) 2 (B) 3 4 (D) 5 4. The function h is given by h(x) = 2: 7 7. Which of the following statements is true? (A) h is equivalent to -12 and has the same end behavior as the graph of y = 2x". (B) h is equivalent to 24 1242x-3 and has the same end behavior as the graph of y = 2x. (C) h is equivalent to " + - and has the same end behavior as the graph of y = 212. (D) h is equivalent to 2 and has the same end behavior as the graph of y = 2x. 5. The rational function / is expressed as the quotient of two polynomial functions f and g by h(x) = 2 . The function f is given by f(x) = 6x3 - x2 + 60x - 25. If the graph of h has a slant asymptote of y = 2x - 1, which of the following describes g ? (A) g has degree 2 with leading coefficient 3. (B) g has degree 2 with leading coefficient 12. C) g has degree 3 with leading coefficient 3. (D) g has degree 4 with leading coefficient 12.5- The rational function h is given by Mac) = W . Which of the following describes the end behavior of h '? AP Preeulculus Page 1 of 5 Test Booklet 3.10 Homework As :1: increases without bound, M30] increases without bound, and as :1: decreases without bound, M22) decreases without bound. (A) As 2: increases without hound, 31(3) increases without bound, and as :1: decreases without bound, h(..":) increases without bound. (B) As .7: increases without bound, 31(1) decreases without boundJ and as .1" decreases without b1::lundJ 171(3) increases without bound. (C) As :1: increases without bound, Me] decreases without bound. and as :c decreases without bound. h($} decreases without bound. (D) 7. -3 -2 -10 X 2 -2 3 -2- -2 Graph of f Graph of g The graphs of the polynomial functions f and g are shown. The function h is defined by h(x) = (2) g(x) What are all vertical asymptotes of the graph of y = h(x) ? (A) = = 2 only (B) r = 3 only (C) = -2 and x = 3 only (D) = = -2, x = 2, and = = 3 9. Which of the following names a function with a hole in its graph at a = 1 and provides correct reasoning related to the hole? Page 4 of 5 AP Precalculus AP CollegeBoard Test Booklet 3.10 Homework (A) The graph of f(a) = has a hole at (1, 2) because the values of get arbitrarily close to 2 for a -values sufficiently close to 1, but the function is undefined at a = 1. (B) The graph of g() = has a hole at a = 1 because the values of increase without bound for I -values arbitrarily close to 1. (C) The graph of h(a) = has a hole at (1, 0) because the values of are arbitrarily close to 0 for -values sufficiently close to 1. The graph of k(x) = (7-1) has a hole at a = 1 because the values of 4x - 4 and (x - 1) are (D) arbitrarily close to 0 for a-values sufficiently close to 1.10. r() 1.997 1.3337 1.998 1.3336 1.999 1.3334 2.001 1.3332 2.002 1.3331 2.003 1.3330 The rational function r is given by r(@) = _r-2 . The table gives values of r(x) for selected values of x. Which of the following statements is true? (A) lim r(x) = 3, so r(2) = 3. 1 +2 (B) limr(x) = = and r is undefined at a = 2, so the graph of r has a hole at (2, 3). C) lim r(x) = 2 and r is undefined at I = 2, so the graph of r has a hole at (2, ). lim r(x) = oo, lim r(@) = oo, and r is undefined at x = 2, so the graph of r has a vertical asymptote (D) x-+2+ at r = 2