5. Solve graphically. Express your answer in interval notation.

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1 PRECALCULUS GROUP REVIEW FIRST SEMESTER 016 Approximate the followin 1- usin: lo 0.6, lo 5 0.7, and lo lo lo 5 lo lo 10. lo 7 4. Find all zeros aleraically ( any complex too) x x 0x 9x 16x Solve raphically. Express your answer in interval notation. x x 5 6. Are these functions inverses?: 5 5 and ( x). x x 7. Given that x 5, evaluate and simplify the difference quotient, f ( x h) h 8. Solve. x x 6 9. Will x 1 have an inverse function? Explain. Find the inverse if it exists. 10. What is ) f (x if x and ( x) x

2 11. Use the Rational Zero Test to determine all possile rational zeros of f. Do not 5 find the actual zeros. f x x x 7x 6 1. Find all the real zeros of the function. f x 45x x 16x 4 1. Find the complete factorization of x 4 9x 4x 6x 16 if is one of the factors. x Find the equation for a paraola with a vertex at (-,) which passes throuh (7,-18). Think aout the standard form. 15. Solve. Round to three decimal places: ln x Solve: 4 1. x 4 x 17. Graph x x 4. Approximate relative minimums and maximums. Use interval notation to descrie intervals over which the function is increasin, decreasin, or constant. 18. Solve y completin the square: 0 x 4x. Show work. 19. Solve 5 x Solve ln( x 1) ln( x ) ln x.

3 1. Write the followin equation in standard form and ive the coordinates of the vertex: x 4x 1.. Let x e the amount, in hundreds of dollars, a company spends on advertisin, and let P e the profit. Be ale to solve ALGEBRAICALLY! a. What expenditure for advertisin ives the maximum profit if P 0 0x.04x?. What is the profit?. Find all zeros of f(x), iven that -i is a zero of x 9x 8x Write the equation of a cuic polynomial with roots of i and Find for the function a. domain: 6x 5 (if they exist) x 9. Vertical Asymptotes c. H.A.: 6. Give a complete definition of a function in your own words. 7. Approximate the intervals over which the function x x 4 is decreasin. 8. Find the inverse of 17 x. 5x

4 0 9. Let ( x) x x x ( x 4) ; x 1 ; 1 x ; x 7 ; x 7 Determine the followin: a. ( ). ( ) c. (7) d. Suppose that y >. Determine ( y+4) 0. Determine if the function ( t) 16t 19t 8 is even or odd and show aleraically. 1. If c(x) is the cost of producin x units, then c(x)/x is the averae cost per unit. Suppose the cost of producin x units is iven y c(x) =.1x 70x + 10,000x and that no more than 00 units can e produced per week. What production level (numer of units produced) should e used in order to minimize the averae cost per unit and what is the minimum averae cost?. The half-life of a certain sustance is.6 days. How lon will it take for 0 rams to decay to rams?. 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. 4. Solve aleraically: t 4 t 8 0.

5 5. Find the x-intercepts of h ( x) x 10x 5 aleraically. 6. Suppose I have a matrix A of order X 4 and matrix B of order 4 X. Which is defined: AB or BA or Both. 7. Use the formula for findin the inverse of a matrix to find the inverse of the matrix (if it exists). L N M 1 O Q P 8. Solve the system of linear equations usin a matrix method. 8x y 7z 16 R S T 4x 4y z 8 6x 5y z 45 [A] 8,, 6 [B] a, a, a [C] [D] ,, 6,, Find the least squares reression line and predict an answer. State Fair Winnin Zucchini Lenths Predict the winnin lenth for the year 000 usin your equation. 40. Write a function, that could possily e a cuic polynomial, with real coefficients and roots of and i.

6 41. Condense the expression to the loarithm of a sinle quantity. 4 lo x 5 lo x [A] lo 10 x x 4 [B] lo x x [C] x x 4 [D] None of these lo Find the value of x lo 6 x 5 4 [A] [B] [C] [D] Determine the interest rate required in order to doule an initial invest of $,000 in 1 years: (Give the percentae accurate to three decimals) a. if the money will e compounded quarterly. if the money is compounded continuously If the center of a circle is at (,4) and has a radius of 5, write the standard equation. 45. Solve lo 15 x