1. Solve for x and express your answers on a number line and in the indicated notation: 2

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1 PreCalculus Honors Final Eam Review Packet June 08 This acket rovides a selection of review roblems to hel reare you for the final eam. In addition to the roblems in this acket, you should also redo all of your eams to identify areas of weakness.. Solve for and eress your answers on a number line and in the indicated notation: (a) < 0 (set builder) (b) 6+ < 0 (interval) Solve for : 3 3. Solve using the geometric definition of absolute value: (a) (b) > 0 4. Factor comletely: (a) + 8y (b) (c) 8 ( ) + 4 ( ) + ( ) (d) ( ) ( + 4) (e) 3 y+ 3y+ 9y+ 7y 5. ì if 6 ï f í ï î+ if ³ 0 ( ) if 6 < < 0 (a) Grah the function. ( ) ( ) ( ) (b) Find f 7 + f 5 f 5. g(4 + h) g(4) 6. For g ( ), evaluate and simlify. h 7. Sketch each grah. State the coordinates of the verte and the equation of the ais of symmetry: (a) y 4+ 4 (b) 4y+ 3y 8. The inequality, is true if and only if (A) or (B) or (C) ³ k k ³ 0 k ³ k k ³k k k ³ k (E) None of the receding a+ b a+ b 9. If is negative, then a+ b a b + ( a+ b) (A) 0 (B) (C) (E) None of the receding

2 0. The length of a rectangle is inches less than three times the width. If the length is increased by 5 inches and the width is decreased by inch. The length will be five times the width. Using to denote the original width, which of these equations can be used to solve for? (A) (B) (C) ( ) ( ) (E) None of the receding. Which of the following is equivalent to? (A) (B) (C) a + b + a b a+ b (E) None of the receding. Let. Then ( a+ b) ( a) + (b) g ( ) ( ) g ( ) g(7) (A) (B) (C) (E) None of the receding 3. Consider the function defined as. What are the domain and range of this function? (A) Domain: ; Range: (B) Domain: ; Range: (C) Domain: ; Range: Domain: ; Range: (E) None of the receding y f( ) Î! y Î! ¹ y ± ¹ y Î! Î! y ± 4. Reduce to lowest terms. (Remember to state restrictions.) (a) (b) (c) (d) (e) h 5 h ( ) (f) (g) (h) (i) 5a 3b 3b 5a ( + ) y y

3 5. Using restriction sets, solve for : 7 3 ( ) Find the remainder if is divided by. 3 ( ) Let. Use synthetic division and the remainder theorem to find (3) ( ) Is a factor of? Show work to suort your answer. 9. What are the ossible rational roots of f 3 ( ) ? 0. Find all real roots of 5 4 ( ) ( ) Find all real and imaginary roots:.. Determine if each function is even, odd, or neither: ( ) f Which of the functions and would make f! g 4? ( ) 4 f (A) ; (B) f 3 ; (C) f 3 ; f 3 ; ( ) (E) None of the receding f g ( )( ) ( ) 3 g 3 ( ) g( ) 4 ( ) g( ) 4 ( ) g( ) ( 4 ) ( f g h)( ) 4. Find where,, and. 5. Find.!! f() æ 3 tanç è 4 ø g ( ) + h ( )

4 6. Which of the following are correct? æ 3 æ 3 æ 3 I. sin ç II. cosç 0 III. tan ç is undefined. è ø è ø è ø (A) I only (B) II only (C) III only I, II, and III (E) None of the receding cos sin 7. Find the general solution of. 8. Which of the following is the general solution of, where? (A) (B) (C) sin + k + k + k k (E) None of the receding 9. Grah cycles of each. State the amlitude (when alicable) and the eriod of each function. a) b) c) d) e) f) k ÎZ y sin y 3cos4 y tan 7 6 y sec5 ycot y csc æ æ sinç arccos ç è è øø 30. Find the value of. (,) 3csc Find all solutions for in the interval. 3. Sketch the region bounded by and. Shade the bounded region and state its boundary oints. 33. y 4 + y 5

5 34. Evaluate each limit: 35. Evaluate each limit: tan3 cos f( + h) f( ) lim lim lim f( ) sin h 0 h f( + h) f( ) æ lim f() lim cos h ç 0 h è ø æ6 limsinç lime è 3 ø a) b) c) when d) when e) f) g) ( ) Show that h ( ) 3 can be written as the comosition of three functions. 37. Find the equation(s) of the line(s) tangent to + y + 6+ y 5 0 when Given f( ), find 3 f ( ). 39. Sketch each function. Include intercets and asymtotes when alicable. State the domain and range for each function. y ( 3) + 4 y ( ) 3 + a) b) c) y 3 y 3 d) e) f) 3 y ( 4) y + 3

6 y + 5 y g) h) i) y y 3+ 7 y j) k) l) + 6 y The foci of an ellise are at (0, ) and (0, 7) and length of the minor ais is 6. Write an equation for the ellise. 4. Let # 8 y # + 6y 3. a. Write an equation of the conic section in standard form. b. Find the coordinates of the center and foci, and equations of asymtotes (if any). c. Sketch the conic section. 4. A circle is centered at (3, 5) and is tangent to y + 7. Find an equation of the circle. 43. Find the inverse of the matri shown below. 44. Find the roduct: 45. Find the determinant: 46. Solve for :

7 47. Use Cramer s rule to solve for and y. 4y y Given the following matrices, Find: a) A B b) AC c) AB A / 0 3, B /0 0 4, C Put the matri into row echelon form: 50. Prove the identity: sin( A B) cot Acot B sin Asin B