PRECALCULUS GROUP FINAL FIRST SEMESTER Approximate the following 1-3 using: logb 2 0.6, logb 5 0.7, 2. log. 2. log b

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1 PRECALCULUS GROUP FINAL FIRST SEMESTER 008 Approimate the following 1-3 using: log 0.6, log 5 0.7, and log log = log log 5 = log log 7 4. Find all zeros algeraically ( any comple too) = Solve graphically. Epress your answer in interval notation Are these functions inverses?: 5 5 = + and g ( ) =. 7. Given that = 3 5, evaluate and simplify the difference quotient, f ( + h) h 8. Solve. 6 = 9. Will = + 1 have an inverse? Eplain. Find the inverse if it eists. 10. Ziggy has a stack of 5 inde cards. With a pair of scissors, he cuts the stack in half and then places all the resulting card pieces in one stack. If he does this a total of four times, how many card pieces will he have?

2 11. What is ( g) () f if = + 3 and g( ) = 1. Write the first five terms of the arithmetic sequence. Find the common difference and the nth term of the sequence as a function of n. a = 8; a = a + 1 k + 1 k 13. Find the indicated nth partial sum of the arithmetic sequence. 5, 13, 1, 9,..., n = Find the sum of the finite geometric series to three decimal places. 1 n n = Use the Rational Zero Test to determine all possile rational zeros of f. Do not 5 3 find the actual zeros. f = Find all the real zeros of the function. f = Find the complete factorization of if 1 factors. is one of the 18. Find the equation for a paraola with a verte at (-3,) which passes through (7,-18). Think aout the standard form. 19. Solve. Round to three decimal places: ln 3 = Solve: = Graph = + 4. Approimate relative minimums and maimums. Use interval notation to descrie intervals over which the function is increasing, decreasing, or constant.

3 . Solve y completing the square: 0 = 3 4. Show work. 3. Solve = Solve ln( + 1) + ln( ) = ln. 5. Write the following equation in standard form and give the coordinates of the verte: = Let e the amount, in hundreds of dollars, a company spends on advertising, and let P e the profit. Be ale to solve ALGEBRAICALLY! a. What ependiture for advertising gives the maimum profit if P = ?. What is the profit? 3 7. Find all zeros of f(), given that -i is a zero of = Write the equation of a cuic polynomial with roots of i and Find for the function a. domain: = (if they eist) 3 9. Vertical Asymptotes c. H.A.: 30. Give a complete definition of a function in your own words.

4 3 31. Approimate the intervals over which the function = + 4 is decreasing. 3. Find the inverse of 17 + = Let 0 π g( ) = + ( + 4) ; < 1 ; 1 π ; π < < 7 ; 7 Determine the following: a. g ( ). g (π ) c. g (7) d. Suppose that y >3. Determine g( y+4) 34. Determine if the function g ( t) + t 8 = 16t 19 is even or odd and show algeraically. 35. If c() is the cost of producing units, then c()/ is the average cost per unit. Suppose the cost of producing units is given y c() = ,000 and that no more than 300 units can e produced per week. What production level (numer of units produced) should e used in order to minimize the average cost per unit and what is the minimum average cost? 36. The half-life of a certain sustance is 3.6 days. How long will it take for 0 grams to decay to 3 grams?

5 37. Determine the interest rate required in order to doule an initial invest of $1,000 in 15 years: i. if the money will e compounded yearly ii. if the money is compounded continuously. 38. Solve algeraically: t 4 t 8 = Find the -intercepts of h ( ) = algeraically. 40. Find the indicated term of the sequence. a a n = 17 = n n For the sequence defined y a n, use sigma notation to write the sum of the first five terms of the sequence. an = n Find the sum of the infinite series A formal garden has shrus planted inside a grid consisting of 18 rows. The first row contains 16 shrus, the second contains 18 shrus, the third 0, and so on. Write an equation epressing the numer of shrus in a row as a function of the numer of the row. Find the numer of shrus in the fifth row. 44. Find the sum of the infinite geometric series A certain sum of money is invested in a usiness. Each year this investment earns 1.5 times as much as in the preceding year. If the investment earned a total of $34,15 in four years, how much did it earn in the fourth year? 46. Suppose I have a matri A of order X 4 and matri B of order 4 X. Which is defined: AB or BA or Both.

6 47. Use the formula for finding the inverse of a matri to find the inverse of the matri (if it eists) Solve the system of linear equations using a matri method. 8 y + 7z = y + z = 8 6 5y z = 45 [B] , 3, [A] 8, 3, 6 [D] a, a, a [C] 6,, Find the least squares regression line and predict an answer. State Fair Winning Zucchini Lengths Predict the winning length for the year 000 using your equation. 50. Write a function, that could possily e a cuic polynomial, with real coefficients and roots of and 3i.