Any help that can be given would be greatly appreciated!

1. Given f(x) = 5x -8 , find f (-4)- f(0) 2. Determine if the function f (x) =- 3x+2 is one-to-one. If it is, find f (x) . 4 3. Find the center and radius of the circle: 2x2 + 2y' +4x-8y -30 = 0x 2 4. Given the rational function f (x) = x 2 - 9 (a) Find any intercepts (b) Determine vertical asymptotes, horizontal asymptotes, and slant asymptotes, if any (c) Test for symmetry (d) Evaluate and show at least 2 solution points for each piece of the graph (e) Sketch the graph of f (x) on the set of axes below: 5. Given g(x) = f-'(x), find g(2) if (i) f(x) =3-4x (ii) f(x) = x+2x-16. Suppose g (x) = x 2 - 1 (a) Find any intercepts (b) Write equations for all vertical asymptotes, horizontal asymptotes, and slant asymptotes, if any (c) Test for symmetry (d) Evaluate and show at least 2 solution points for each piece of the graph (e) Sketch the graph of f(x) on the set of axes below:7. Find the quadratic function that has vertex (1, 3) and whose graph passes through the point (-1 2) 8. Write the partial fraction decomposition and simplify your answer completely: 3x2- 7x-2_ x - x 9. Find a third degree polynomial f(x) with integer coefficients that has zeros: -1, 1 - 3,1+ V310. Write the partial fraction decomposition and simplify your answer completely: 3x2 + 4x+4 x' + 4x 11. With the aid of the table below apply the Intermediate Value Theorem to estimate the zeros of f(x) =-x +3x2 +9x-2 in the closed interval [4, 5]. (Write your answer to the nearest tenth). X f(x) 12. Find the remainder r(x) = 2x+ 3 k when f(x) =6x +7x2 -15x+6 is divided by 2x+3 (Leave your answer as a fraction in simplest form).13. Divide 3x*+9x -16x -18x2 + 32 by x+ 2. (Leave your answer in division algorithm form) 14. Solve the inequality and graph the solution on the number line: 5 - > 3 x - 2 x+2 Clearly show all critical numbers, test intervals, and solution interval(s). 15. If f(x) =~ x-5 and g(x) = V2x2 +7, evaluate (f . g)(-3).16. Find the remainder in simplest fractional form when f(x) =6x3 +7x2 -15x+6 is divided by x2 +2 17. (a) Write the function g(x) =-x + 2x +5 in standard form. Hint: Complete the square of g(x) (b) Determine coordinates of the vertex and all intercepts (as ordered pairs). (c) Write an equation for the axis of symmetry. 18. Write the system below as an augmented matrix; use your calculator to solve the system, and write you answer as an ordered quadruple. Show the identity & constant matrix in the rref operation: y+ z - 2w =-3 x+2y-z = 2 2x+4y+ z-3w= -2 x- 4y-7z - W =-1919. (a) If x - 2 is a factor of the cubic polynomial p(x) = 2x' + x2 - ax +6, find the value of a, and write the polynomial p(x) with numerical coefficients. (b) Hence, factor the polynomial completely (c) Find the zeros of the polynomial (d) Find the remainder when p(x) is divided by x +8 Test algebraically to determine whether the function f(x) = x(x + x) is even, odd, or neither.21. Suppose f(x) =3-4x and 8(x) =- 3 -x 4 , test for one-to-one and prove by composition of functions that f(x) and g(x) are inverses. Justify your conclusion. 22. Two matrices are defined as A= 4 - (2 7 ) and b - 2. Complete the matrix operations algebraically : (a) A+B= (b) 3A-2B = (c) AB = (d) BA = 23. lim- 2x cotx = x-+0 sin xIn 24 - 26, insert the required factor in the parentheses to complete the identity: Show clear steps. 24. 3(2x+1)x/2+4x3/2 = 201/2( 25. 1 2Vx + 5x3/2 - 10x5/2 = - 2 VX 26 . - ( 2x + 1) 5/2 - 1 ( 2x + 1) 312 - ( 2x + 1 ) 3/2 15 - C\f29. Simplify the algebraic expression completely and leave your answer in simplest radical form: x' (x+ 1) 45 - x2(x+ 1) 13 x 2 30. Write the denominator as a difference or sum of squares and simplify completely: 4 4x2 + 4x-3 3 ( b ) 3x2 +6x+15 31. Find the solution(s) of the equation in the interval [0, 2x ) algebraically: sin ( x+ 7 )+ sin ( x -7 =132. Verify the identity: cos(x + y) cos(x - y) = cos x - sin y 33. Suppose f (x) = 2x+1, x 2 . Find Him f (x) if the limit exists. 34. Suppose f(x) = -. Find lim f(x) if the limit exists. x - 235. Suppose f(x) = X, * * -1 1, x =-1' 121 (*) if the limit exists. 36. lim 3- Vx x -9 x-9 37. Suppose f(x) = e* , find lim im f(xth) - f(x) h , if the limit exists. 38. For the function given by f (x) = x2 -1, evaluate lim f(x) -f(3) x -+ 3 x - 3x +1 39. Find lim (if the limit exists) 40. Given log, 2 =0.2789 and log, 3=0.4421, find log. 8 36 41. Use the definition of continuity to determine the value of c so that f (x) is continuous at x = -1 for f (x ) = _Jx+3, x5-1 2x - C, x>-1 42. Solve for x in 2"= e . Leave your answer in the simplest natural logarithmic form.43. Identify the type of symmetry: x y2 + xy = 5 44. Find all vertical and horizontal asymptotes of f (x) = In x In x' - 1 45. Evaluate and write an algebraic expression for tan [arcsin x]46. Solve for x: In ex-1 = 26 47. Solve for x algebraically and check your answer with a calculator: In (2 + x) + In(x -1) = In(4x) 48. Assume the radius of the earth to be 4,000 miles; find to the nearest hundredth, the distance between two cities on the same meridian, located on the given latitudes: Dallas 32 47'9" N Omaha 41' 15'42" N Omaha Dallas 10 Note: This Review Packet is not exhaustive: In addition to your preparation for this final, review your notes, worksheets, homew