2018 Pre-Cal Spring Semester Review Name: Per:

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1 08 Pre-Cal Spring Semester Review Name: Per: For # 4, find the domain of each function. USE INTERVAL NOTATION!!. 4 f ( ) 5. f ( ) 6 5. f( ) 5 4. f( ) 4 For #5-6, find the domain and range of each graph y y Use the following information for #7-8. f ( ) 0 7 g ( ) 4 7. Find f( + ) 8. find g(-4) 9. Write an equation for the line passing through the given point (-5, ), and perpendicular to the line with the equation y 5 = Write the equation of the vertical line through the point (4, ). A. = B. y = C. = 4 D. y =

2 . Draw 5,. Find the magnitude and the direction of the vector.. a, 5 v,5. Find a v. Given: a, b 7, and the angle between them when placed tail to tail is 5 o. Find a b the resultant vector makes with a. and the angle that 4. a =7 and has a direction of 40. Resolve a into its horizontal and vertical components in eact values and approimate to three decimal places. 5. Convert 5, 6 to rectangular form. Find the eact values. A., B., C., D.,

3 6. Convert (-,6) to polar form in radians. Round to three decimals. A. (5.657, 7.565) B. (.49, 6.5) C. (.57, -0.79) D. (.49, 6.5) 7. Name the given points two ways, using positive and negative angle (in radians). P A T A P 8. using the graph from #7, plot the points. T 0 B, 6 C, 4 D 0, 47 7 For #9-0, describe the transformations of the graph from f ( ). 9. f ( ) 7 0. f ( ) 4. Write the equation in standard form ais of symmetry? f ( ) 0 f ( ) a h k by completing the square. What are the verte and

4 Use the following function for # -5 f ( ) 5 g ( ) 4 h ( ) 5 Write the following functions in simplified form and state the domain.. f g. f g 4. f h 5. g h Use the following functions for # 6-8. f ( ) g( ) 7 Write the following functions in simplified form and state the domain. 6. f g 7. g f ( ) 8. f g (0 Perform the indicated operations. 9. ( 9) ( 6 5 8) 0. ( )( 4 5). ( 6) ( 6) A. + B. + 7 C. + 6 D. 6 Factor completely with respect to the integers:. 7 8y. 6 4m m 0

5 y Factor completely with respect to the integers: 4. 4 a a k 56k Find the quotient and remainder using long division: Find the remainder of: Is a factor of f ( ) 5? 9. The graph of f ( ) a b c d e (where a, b, c, d, and e are real numbers) is shown below. How many real and imaginary zeros does f() have? A. real, imaginary. B. 4 real, imaginary. C. real. D. 4 real. 40. Find all real zeros and write the polynomial as a product of linear factors. f ( ) 4

6 4. Given: f 5 ( ) a. What is the degree of f()? b. How many total zeros does f() have? c. What is the left end behavior? d. What is the right end behavior? e. What is number of maimum turns? f. Does the graph pass through the origin? g. True or False: The Domain is,. h. True or False: The Range is,. i. What is the y-intercept? j. Find all real zeros. 4. Write an equation with degree of whose zeros are 4 and. A. ( 4) ( ) B. ( + 4) ( + ) C. ( 4) ( ) D. ( 4) ( ) 4. How many times is 4 a root of Support your answer with algebraic proof. A. time B. times C. times D. 4 times ? Find the domain, vertical asymptotes, and end behavior for: 44. f( ) 5 Find the end behavior asymptotes for: 45. f( ) 46. f( ) 0 7

7 Identify all indicated information. 47. f( ) 0 5 y-int: -int: VA: Hole: HA/SA: 48. y As, f ( ), f ( ) +, f ( ), f ( ), f ( ), f ( ) Solve the inequality using interval notation Solve for : round decimal places log 5 5. log log 55. log log 64 log 5

8 56. log 4 log 4 log log log log log Which function is equivalent to f( ) 5? A. g( ) 8 5 B. g( ) 8 5 C. g( ) 5 D. g( ) 5 E. g( ) 5 Evaluate: log log log log 9 e ln 7 Use the following information for Questions 6-64: Use the formula: y Ce kt. Round to decimal places 6. The ½ life of a certain substance is 8 days. If there are 8. grams initially, when will there be 0.5 grams left? 64. An isotope of sodium has a half-life of 5 hours. How many hours will it take for 40% of a given amount to remain?

9 Use the following information for Questions 65-68: If an initial principle, P, is deposited in an account that pays interest at rate r, compounded n times per year for t years, then there will be a final balance, A. Round to decimal places r A P n nt or A Pe 65. What is the total value after 7 years of an initial investment of $550 that earns interest at the rate of 6.%, compounded monthly? rt 66. A $500 investment earns interest compounded quarterly. Determine the interest rate needed in order for the money to grow to $4000 over the course of 4 years. Round to decimal place and give the percentage. 67. How long will it take an investment of $00 at 7.45% APR to grow to $500 if the interest rate is compounded monthly? Round to decimal place. 68. How long will it take an investment of $000 to double when invested in an account earning 4.75% interest compounded continuously? Round to decimal place. Write all your answers as simplified radicals and fractions. NO DECIMAL ANSWERS! (Use your formula chart, you will be given a blank one for the test) 69. Find the center and radius of the circle: y y A. Center (, ), radius = 6 B. Center (, ), radius = C. Center (, ), radius = 4 D. Center (, ), radius = Find the verte, focus, and directri of the parabola: Is this parabola horizontal or vertical? 4 4 4y 6 0

10 7. Find the center, vertices, co-vertices, and foci of the ellipse: y Is this ellipse horizontal or vertical? Find the center, vertices, and foci of the hyperbola: Is this hyperbola horizontal or vertical? 4 y 8 4y Write the equation of a circle whose diameter has endpoints 5, and, Write the equation of the parabola verte (, -) and directri 5. Is this parabola horizontal or vertical? FIND THE EXACT VALUES: sin 6 A. B. C. D. 76. cos A. - B. C. undefined D sec A. B. C. D.

11 Sequences, Series Formulas a a d n n n an a( r) Sn af al n S n a F n r a S F r r Decide if each of the following sequences are arithmetic, geometric or neither. 78.,,8,, ,8,4,40, ,,,6,4... Write the nth term formula and find the indicated term for each sequence. 8. The sequence is arithmetic. a8 and a9 0. a4? 8. The sequence is geometric. a 8 and a9 768, a5? Find the sum of each series if it eists. MUST USE FORMULA! 0 n 84. n n n n n 86. n0 4 n 87. Black Gold drilling company charges $0 to drill the first foot of an oil well, an additional $0.50 for the second foot, an additional $.00 for the third foot, and so on. How much would it cost to have the Black Gold drilling company drill a 00 foot well?

12 Miscellaneous: 88. Complete the following statements with a sometimes, always, or never: a) A polynomial function has domain. b) A polynomial function has range. c) A rational function has domain. d) A rational function has range. 89. True/False a) If is a zero of f(), then (-) is a factor of f(). b) f( ) 4 5 has a horizontal asymptote at y=0. c) All infinite geometric series have a finite sum. d) ln e e) log y log log y f) ln e g) log( 4) does not eist h) ln e