~t-,a~p.--e;;;;;i71- 0) x+ x2-sx+6. x x-38. PRECALCULUS Semester 1 Review

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1 PRECALCULUS Semester 1 Review PART 1: CALCULATOR ALLOWED 1. If fix) = 1-x and [1 is the inverse off, how many solutions does the equation f(x) =[1 (x) have7 A) None B) One C) Three 0) Five Summer The PTSA members are placing boxes around the school to collect toys for a toy drive. To make a toy drive box, they start with a square sheet of cardboard with sides 8 feet long. They cut congruent squares from each corner of the cardboard sheet, then fold the sides up and tape the cut edges together, as shown.. The price P, in dollars, of a certain product and the quantity x sold obey the demand equation P = 1 X ~ x ~ Suppose that the cost C, in dollars, of producing x units is C = Assuming that all items 5 produced are sold, find the cost as a function of the price. ~t-,a~p.--e;;;;;i71- &7 -;"ape tape tape. What are the possible rational roots of fex) = x + x x 17 The volume of a box depends on the size of the squares that are cut from the corners of the square cardboard sheet. Let V represent the volume of one of the boxes and x represent the length of one side of the smaller square cut from the corners ofthe larger square. Write a rule that expresses Vas a function of x.. Find the domain of each of the following functions: -X A) fex) = (x+)(x-5) 8) fex) = (x+)(-x) 7. Let 0 be the origin and P be a point on the terminal side of e, an angle in standard position. Find the coordinates of P when OP = and e 51, correct to three decimal places. 5. Use long division to divide :_8. x -Sx+6 A) X + 5 B) C) x x-8 x+zx+8 x- x -5x+6 5x-6x-8 0) x+ x-sx+6 8. Given a point pe-5,1) on the terminal side of (), an angle in standard position, find the exact value of cos e. 1 A) - 1 B) C) ) ~--~

2 PRECALCULUS Semester 1 Review Summer Convert of the following angles to radians: A) 5 PART : NO CALCULATOR 15. Which statement describes what happens to the graph of y = a(x - h) + k when the value of h is changed from 5 to -? A) The graph translates 7 units down B) The graph translates 7 units up C) The graph translates 7 units left 0) The graph translates 7 units right 10. Convert each of the following angles to degrees: A)!!!. 6 B) _1_11: C) 511: 711: D) - z 11. Determine one positive and one negative coterminal angle for each of the following: A) f) = B) f) = -70 C) e= ; 0) f) = _ 1911: 16. The functions f(x) and g(x) are defined in the function tables. The function g(x) is a transformation of f(x). Which of the following best describes g(x) in terms of f(x)? x f(x) A - 6 B a C E 5 a I AJ g(x) = {(x - ) - BJ g(x) = I(x + ) - C) g(x) = {(x - ) + D) g(x) = {ex + ) + I I x g(x) A' 1 Bf 1 C' D' 5 E' 8-1. Find the length of the arc with radius of feet generated by a central angle of Use the table below to help you create a table of values for each transformation of {(x). 1. Find the central angle that generates an arc of length 78 meters with a radius of 6 meters. A) Y -{(x) B) y = {(x ) C) y = lex + ) 1. Find the real zero(s) of the function (round to decimal places). I(x) = x 16x +.5x

3 PRECALCULUS Semester 1 Review Summer If [(x) == x 7 and g(x) == -8x 9, find: A) (f + g)(x) B) (f g)(x) C) (g f)(x) D) ([. g)(x) 1. If [(x) = and g(x).!., identify the x+ x domain of the function defined by (f 0 g)(x). A) (-00,_1/ ) u (-lh,oo) B) (-00,0) U (0,00) C) (-00, -) U (-,0) U (0,00) D) (-oo,-lh) U (_1/,0) U (0,00) 19. Classify the functions as even, odd or neither.. The inverse of a function is[-l(x) = J/ 5X. What is the original function? A) [(x) = x + 1 B) [(x) = - C) [(x) == x S + x. Use the tables to find each value. f~) I 1 J D) [(x) Ixl E) [(x)=x -x g;x) I 7 I F) [(x) =-- 1 x A) [(g()) 0. Evaluate the expression (f 0 given in the table. g) () using the values B) g([(5)) = C) [(g(6)) = x - 0 f(x) 7 5 g(x) 1. Given that [(x) =, what is [()? A) - B) C) 0 D) 5. Given [(x) = ~ and g(x) =../x -, state x the domain of: A) [(g(x)) B) g([(x))

4 PRECALCULUS Semester 1 Review Summer Which of the following is a zero of y = x + 9x - x - 10? A) - 0. Suppose that this is not a complete graph of a particular function. Instead, the function also has a local minimum at x =. What might be true about the function? B) C) D) 5 7. Which of the following is equivalent to the expression (x- )7 A) CoX(-)o + C1X(-)1 + Ci(-) + C~1(_) + C~o(-) B) CoX (-) + C1X1(-) + CX(-) + CX(-)1 + C~(_}o C) CO(X - ) + Cl(X - ) + C(X ) + C(X - )1 + C(X - ) D) C O (X ) + Cl(X - )1 + C(X - ) + C(X - ) + C(X - ) 8. What are the eros of the polynomial? y = x + X - 19x + 6 A) It could be a rd degree polynomial, but with a positive leading coefficient B) It could be a rd degree polynomial, but shifted right units C) It could be a th degree polynomial with a positive leading coefficient D) It could be a th degree polynomial with a negative leading coefficient 1. Based on the behavior you see in the scatterplot, which might be an appropriate polynomial model to try as a fit for these data? 9. Which of the following functions could represent the graph: 6 Y 5 1 Y x A) [(x) = x(x )(x 7) B) [(x) = 1.x Z (x - ) (x - 7) A) [ex) == x + 5x - 5x - 6 B) [ex) = + Sx + 5x - 5x - 6 C) [(x) = X + 5x + 5x - 5x - 5 C) [(x) = -x D) [(x) =.x (x )(x 7) D) [(x) = X + 5x + Sx - 5x - 6

5 PRECALCULUS Semester 1 Review Summer 015. Which of the following best describes the graph of the function ex) =? x -Sx- A) The graph has a removable discontinuity at x and a vertical asymptote at x -Y>. B) The graph has a vertical asymptote at x = and a removable discontinuity at x = -Y>. C) The graph has a removable discontinuity at x = and x = -Y>. D) The graph has a vertical asymptote at x = and at x -Y>.. Solve the given inequality: A) _6_ > 1 x+ 6. Find all the zeros of [Cx) = x Describe the end behavior of the graph of [Cx) = (x + )(x - 1)ex + )(x - 5) 8. Which angle of rotation is NOT coterminal with a 0 0 angle? A) -0 0 B) -0 0 C) 90 0 D) B) x + x > x + 1. Find the horizontal asymptotes, if any, of the function x-l [ex) = -. x -x A) x = 0 B) y =0 C) x=l 0) Y = 1 9. Evaluate ~ach of the following without using a calculator: 7rr A) cos 6 B) sin 15 C) tan 15 0 Srr D) csc E) sec (_ ;) 5. Sketch the graph of [ex) = a calculator. without using 0. ' n: A) GIven tan -.078, find tan 8;. s. B) Given sin":::' = 0.09, find x between ~ and n 10 such that sin x = C) G Iven ' t h at cos- rr = --, Y6+{ f' In d t h e exact va I ue 0 f : 1 i. COS llrr 1 ii. cos 1rr 1 iii. cos rr 1 5 """"-~""~ ~

6 PRECALCULUS Semester 1 Review 1. If Y = sin(x) - 1, what is the range of the function? A) {y I - ::; y ::; } B) {y I - 1 ::; y ::; } C) {y I - ::; y ::; } 0) {y lye IF!.} Summer What is the equation for the graph shown below? -tr -Jf -. What is the phase shift of the function y = - cos (x -~) A) to the right B) to the left C) 1"[ to the right 0).:::. to the left. What is the period of the function y = sin(x) -? A) y sin(7x) B} y = sin(x) C} y = singx) 0) y sin Gx) - A) - 1"[ B} - 1"[ C) '1"[ 0) 1"[. Which of the following is NOT a function rule for the graph shown?..,.. T -. -, ff. 7 T A) Y = sin(x) + 8) Y = cos ( (x - ~)) + C) y = sin(x + rr) + O} Y = sin(x + rr) + 6