Math120R: Precalculus Final Exam Review, Fall 2017

Transcription

1 Math0R: Precalculus Final Eam Review, Fall 07 This study aid is intended to help you review for the final eam. Do not epect this review to be identical to the actual final eam. Refer to your course notes, in-class test reviews (posted on the precalculus homepage), homework, worksheets, and Webassign problems as well in preparing for the final eam.. The equation of the line passing through the ordered pair,0 4y is: a and parallel to the line y a 4 4 y a 4 y a 4 4 y 4 4a y a 4 4. The police can determine the speed, S, that a car was traveling from the length of the skid mark, L, that the car leaves. Assuming S varies directly with the square root of L, epress S as a function of L. S L kl S L k L L( S) ks S L k S L( S) ks

2 . The distance traveled by a falling object is directly proportional to the square of the time it takes to fall that far. If the object falls 00 feet in.5 seconds, how far does it fall in 5 seconds? 800 feet 400 feet 5 feet 50 feet 00 feet 4. Find the center and radius of the circle with equation given by 9 y 4 5 Center: 9,4 Radius: 5 Center:, 4 9 Radius: 5 Center: 9,4 Radius: 5 Center: 9, 4 Radius: 5 Center: 9,4 Radius: Find the domain of the function gt 4t 5 t,5 5,,0 0,5, 0,5 5,,0 0,5 5, f 6. Let 4 4 Find the y intercept of f( ). 0, 0, 4 0, 4 0, None of these

3 7. Let f ( ) 4. Find and simplify f h f. h 4h h 9 4h 4 None of these Problems 8 and 9 refer to the graph of the function y f t shown below Determine the interval(s) where t 0 f. 4, 0 4, 5, 4, 5 5,, 5, 0 9. Determine the average rate of change of t f from t to t

4 Use the table of values for a function f( ) below to answer question f( ) If f( ) is an even function, what is the missing value in the table? Consider the functions f and g in the tables below. f () g() Which ONE of the following epresses the correct relationship between f and g? g f g f g f g f g f

5 . If the point, the transformation y f 8 is on the graph of f( ), find the corresponding point on the graph of. 6,6, 8, 6 8,6 4 6,. If the domain of f is 5,8, what is the domain of the function f 7,6,9 7,7,0 4,6 y? 4. Let f and g. Find and simplify g f completely. 5. Let f t t. Find f

6 6. The function f b S gives a student s score on a standardized test as a function of the number of books b the student has read. If S is invertible, what is the meaning of f 5? 0 5 The student s score increases by for every additional book the student reads. 0 When the student s score is 0, the student has read 5 books. 0 The student s score increases by for every additional book the student reads. 5 When the student s score is 5, the student has read 0 books. There is not enough information to determine the meaning. 7. The hypotenuse of a right triangle is four times its base. If b is the base of the triangle, epress the area A of the triangle as a function of b. A A b 5 b A b A 5 b A b 8. Determine whether f ( ) 6 k the maimum or minimum value. has a maimum or minimum value, and determine Maimum value: k Minimum value: k Maimum value: Minimum value: Minimum value: 9 k 9 k 9 k

7 9. Which ONE of the following represents the complete factorization of 7 6 6? Suppose the graph of a polynomial function y f () has the following end behavior: y as y as Which ONE of the following statements must be true? The degree of f () is an odd number. f () is an even function. f () has a minimum value. The range of f () is all real numbers. The leading coefficient of f () is a negative number.. Solve for : 6 0 0, 6, or only 6 only 0 or 6 only only 6 or only

8 . Find the value of A so that 4 4 A y is the horizontal asymptote of g A 4 A 7 A. A None of these. Suppose 6 is a vertical asymptote of a function y f ( ). Which ONE of the following must be a vertical asymptote of y f ( )? 8 6 Questions 4 and 5 refer to the function 7 0 f ( ). 4. Find the zero(s) of f. 5 and 4 only only 5, and 4 only 0 only 0 only 5. Find the horizontal or slant asymptote of f. y y y 0 y y

9 6. Find the value of p so that the vertical asymptote of f 6 p 4 p is 5. 0 p p 0 5 p 4 p 0 None of these t 7. The range of f t 00 is:,,0,00 00, 0, 8. Find the inverse function of h ( t) 7 9. h t) log t 7 ( 9 ( 7 h t) log ( t 9) t h ( t) 9 7 t ( 7 h t) 9 log ( t) h ( t) 7 t 9

10 Use the following information to answer questions 9 and 0. The velocity of a skydiver, in feet per second, t seconds after jumping out of an airplane, is v t a e bt, where a and b are positive constants. modeled by the function 9. Based on this model, what happens to the skydiver s velocity as t? The skydiver s velocity approaches: a b a b a b 0. Assume that a 00. If the skydiver s velocity is 70 feet per second after 0 seconds, determine the eact value of b. ln 0 b 70 ln 0.7 b 0 ln 0.7 b 0 ln 0. b 0 ln 0. b 0 Problems and refer to the function f. Find the domain of f. ( ) log. 7,, 0,,,. Find the eact zero of f log None of thes

11 . Simplify the epression completely: ln(4e ) 4 ln( 4) ln( ) 4 ln( 4) ln( 4) e 4. Solve for : log log 4 4 only 4 or 7 only only 4 only only 5. Let tan w, 5 cos w. where the terminal point of w is in Quadrant I. Find the eact value of 5 cos w 9 cos w cos w 9 cos w 5 cosw 5

12 Problems 6 and 7 refer to the following information. Suppose a real number t determines the terminal point a, b on the unit circle. See the graph below. 6. Find the terminal point determined by the real number t. ba, ab, ab, a, b a, b 7. Find t sin. b a b a None of these 8. Find the terminal point, y on the unit circle determined by the real number,,, t. 4,,

13 Problems 9 and 40 refer to the graph of f t A Bt C sin, shown below Determine the value of B. B B ( C) B 6 B B 40. Determine the value of C. C 6 C 0 C C 4 C 5 4. In a certain region of Australia, the population of a particular type of kangaroo is modeled by the function P( t) 00 40sint, where t is measured in years. According to the model, what is the maimum kangaroo population? There is no largest number.

14 4. The minimum value of g( ) 7cos( ) is: Which ONE of the following is a vertical asymptote of the graph of f ( ) tan? The domain of f t cos t is: 0,,, 0,, 45. Simplify the epression tan sin. Assume

15 46. Suppose cot 0 and sec 0. In which quadrant could terminate? Quadrant I Quadrant II Quadrant III Quadrant IV 47. Find the length of an arc that subtends a central angle of 5 in a circle with radius 5. The length of the arc is: The volume of a cone, shown below, is given by V r h. Epress the volume as a function of. 6 sin cos V 64 sin cos V 64 cos sin V 6 V sin cos 6 cos sin V

16 49. Use the angle.8 to determine the eact value of in the figure below sin.8 cos.8 4 4tan.8 4 sin.8 4cos Which ONE of the following angles is coterminal with 45? Let cos Determine the value of cos

17 5. Simplify the epression sin Acsc A sin A cos A. sin A sin A cos A 5. Let sin A where A terminates in Quadrant I, and let cos B, where B terminates cos A B cos Acos B sin Asin, find cos( A B). in Quadrant IV. Using the identity B Suppose sin, where terminates in Quadrant III. Using the identity sin sin cos, sin. find \

18 55. Solve for t : cos t 0 on the interval 0t. 5 t 0, t, t, or t only. t 0 or t only. 5 t or t only. t or t only. 6 6 t 0, t, t, or t only Solve for : sin 0 cos on the interval 0 only 6 tan only 0 only sin only No solution