Exam Name___________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use the graph of the quadratic function to determine the sign of the leading coefficient, the vertex, and the equation of the axis of symmetry. 1) 1) 6 y 5 4 3 2 1 -6 -5 -4 -3 -2 -1 -1 1 2 3 4 5 6 x -2 -3 -4 -5 -6 A) Negative; (3, -2); x = 3 C) Positive; (3, -2); x = 3 B) Positive; (-3, -2); x = -3 D) Positive; (3, -2); y = -2 Determine the vertex of the graph of f. 2) f(x) = (x - 6)2 - 4 A) (6, -4) 3) f(x) = 2x2 + 12x + 22 A) (-4, 3) 2) B) (4, -6) C) (-6, -4) D) (-4, 6) B) (4, -3) C) (-3, 4) D) (3, -4) 3) Solve the quadratic equation. 4) 2x2 + 6x = -2 A) -3 5 2 4) B) -3 13 2 C) -6 5 2 D) -3 5 4 Solve the inequality. 5) x2 + 9x + 20 0 A) x -4 6) x2 + 4x - 5 > 0 A) x < -5 or x > 1 5) B) x -5 or x -4 C) -5 x -4 D) x -5 6) B) x > 1 C) -5 < x < 1 D) x < -5 State the end behavior of the graph of f. 1 7) f(x) = 7 - x2 6 7) A) Up on left side, down on right side C) Up on both sides B) Down on left side, up on right side D) Down on both sides 1 8) f(x) = 3x - 1 3 x 6 8) A) Down on both sides C) Up on both sides B) Up on left side, down on right side D) Down on left side, up on right side Evaluate the function f at the indicated value. 9) x - 8, if x < 5 f(0) for f(x) = 4 - x, if x 5 A) -8 B) -3 9) C) 4 D) -1 Find the domain of f. 17 10) f(x) = 11 - x A) {x | x 17} 10) B) {x | x 17} C) {x | x 11} D) {x | x 11} Find any vertical asymptotes. (x - 2)(x + 7) 11) h(x) = x2 - 9 A) x = -2, x = 7 11) B) None C) x = 3, x = -3 D) x = 2, x = -7 Find the horizontal asymptote of the given function. 6x2 - 4x - 5 12) h(x) = 7x2 - 5x + 7 A) y = 0 12) B) y = 6/7 C) None Use the given functions to find the requested function. 13) f(x) = 9x - 6, g(x) = 4x - 8 Find f - g. A) 13x - 14 B) 5x - 14 14) f(x) = 3x + 6, g(x) = 2x2 Find (fg)(x). A) 6x2 + 12x D) y = 4/5 13) C) -5x - 2 D) 5x + 2 14) B) 6x3+ 12x2 C) 6x + 12 D) 2x2 + 3x + 6 15) f(x) = 2x + 9, g(x) = 5x2 Find (f + g)(x). A) 10x3 + 45x 15) B) 2x + 9 + 5x2 C) 2 2x + 9 5x2 D) 2x + 9 - 5x2 Complete numerical representations for the functions f and g are given. Evaluate the expression, if possible. 16) (fg)(6) 16) x 1 6 8 12 f(x) -3 8 1 13 x -5 -3 1 6 g(x) 1 -8 6 8 A) Undefined B) 1 C) 6 D) 8 Find the indicated composite for the pair of functions. 5 7 17) Given f(x) = and g(x) = , find (f g)(x). x-4 3x A) 15x 7 + 12x B) 17) 5x 7 - 12x C) 7x - 28 15x D) 18) Given f(x) = -2x + 2 and g(x) = 4x + 2, find (g f)(x). A) 8x + 10 B) -8x - 6 C) -8x + 10 Find a symbolic representation for f-1 (x). 19) f(x) = 6x + 3 x A) f-1(x) = - 3 6 18) D) -8x + 6 19) x+3 B) f-1 (x) = 6 x-3 C) f-1(x) = 6 20) f(x) = 15x 7 - 12x D) Not a one-to-one function 2 x+3 20) -3x + 2 A) f-1(x) = x 3 + 2x B) f-1 (x) = x C) Not a one-to-one function D) f-1 (x) = x 3 + 2x Use the compound interest formula to determine the final value of the given amount. 21) $360 at 7% compounded continuously for 8 years A) $630.24 B) $1128.86 C) $38,283.36 22) $12,000 at 8% compounded quarterly for 6 years A) $7301.25 B) $18,922.79 21) D) $863.60 22) C) $19,042.49 Find either a linear or an exponential function that models the data in the table. 3 4 23) x 0 1 2 y 7 21 63 189 567 1 A) f(x) = 14x + 7 B) f(x) = 7(3)x C) f(x) = x+7 14 3 D) $19,301.25 23) D) f(x) = 3(7)x Solve the equation. 24) 2 x = 830 24) A) x = log 830 B) x = 415 C) x = log 830 2 B) x = log -733 3 733 C) x = log 3 D) x = log 415 25) 3 x = 733 25) A) x = log 733 3 D) x = log 2199 Solve the equation symbolically. 26) log3 x = 1.5 A) x = 3 1.5 27) 6 ln x - 8 = 3 1 A) x = e11 6 26) B) x = 1.5 log3 1.5 C) x = 1.5 3 D) x = 1.53 27) 11 C) x = ln 6 B) x = e11/6 1 D) x = ln 11 6 Use the change of base formula to approximate the logarithm to four decimal places. 28) log8.3 221 A) 2.3444 B) 2.5508 C) 0.3920 28) D) 26.6265 Expand the expression. 29) log6 xy 29) A) log3 x + log3 y B) log6 x - log6 y C) log3 x - log3 y D) log6 x + log6 y Use common or natural logarithms to solve the exponential equation symbolically. 30) 5 (12 - 4x) = 1 log 5 A) x = + 12 log 1 31) 4 (5 - 3x) = A) x = C) x = log 1 B) x = - 12 log 5 log 1 C) x = 3 4 log 5 30) log 1 D) x = - 3 + log 5 1 256 31) ln 4 + 15 ln 256 3 ln 256 5 ln 4 Solve the logarithmic equation symbolically. 32) 66 + 8 log x = 50 A) x = -102 B) x = 10-2 B) x = ln 4 -5 ln 256 D) x = ln 256 5 + 3 ln 4 3 32) C) x = -20 D) No solution 33) ln x + ln x5 = 6 A) x + x5 = e6 33) e5 C) x = 6 B) x = e6/5 4 D) x = e Answer Key Testname: REVIEW 3 (1710) F10 1) C 2) A 3) C 4) A 5) B 6) A 7) D 8) B 9) A 10) D 11) C 12) B 13) D 14) B 15) B 16) B 17) D 18) C 19) C 20) A 21) A 22) D 23) B 24) C 25) A 26) A 27) B 28) B 29) D 30) C 31) D 32) B 33) D 5