1 . Let f(x) =-x(x-3)(x+2)(x-5) (a) What is the degree of the polynomial? (b) Find all the zeros of this polynomial and state their multiplicities. (c) Use this information to sketch the graph of f. 2. (a) Find a polynomial f(x) of degree: 3 with zeros: -5, -4, and 1 such that f(-6) =28. (b) Find the equation of the polynomial f(x) graphed on the right. The degree of this polynomial is 6 and f(1) = 100. Leave the answer in factored form. 3. Find all solutions of the following equations by hand (without using a calculator): x' -8x3 +8x+24 =0 given that 6 is a solution of this equation. 4. Find the quotient and the remainder if f(x) =3x' +4x* + x+7 is divided by p(x) =x3 +1 5. Graph each of the following rational functions. List any asymptotes, holes, and the x- intercepts and the y-intercepts. (a) f(x) = 3x - 2 x+4 (b) f ( x) = 2x- - x -3 x-2 (c) f (x) = 2x- +4x -48 x- + 3x - 10 6. Sketch the graph of each function using the following steps: (i) Identify and sketch the graph of the parent function (ii) Indicate how the parent graph is transformed Sketch the graph of the function, including the asymptote. (a) f(x) =273-4 (b) f(x) =-2log, (x+3)7. Expand the following expression as a sum and/or difference of logarithms: x5 Vx+1 logs y ( x- 1) 8. Condense the following expression into a single logarithm: 2In(x-3) - -In(x+2) +4Inx-Iny 9 For each of the following equations, find the exact solution and a decimal approximation rounded to 3 decimal places. (a) 23x+3 1 8 (b) 6"=50 (c) 32-1 =5x+2 (d) log3 x + log3 (x+6) =3 (e) log4 (x -1)- log4 (x+6) = log4(x -2) -log4(x+3) (f) 52x + 125 = 30(5" ) 10. In which quadrant will @ lie if esco > 0 and cose 0. 2 12. In the right triangle ABC with C =90, find all the missing parts if: b = 305 cm, B = 24.90 13. A ladder is leaning against the top of a 7.0-foot wall. If the bottom of the ladder is 4.5 feet from the wall, what is the angle between the ladder and the wall? (Assume the wall is vertical and the ground is horizontal.) 14. Find the exact value of: (a) sin 3 (b) cos _ (c) tan 3300 (d) cot 3 (e) sec 4 15. Verify each identity. (a) (1-sine) (1 + sin @) = cos' 0 (b) secx - cosx = sin x tan x (c) 2 cosx = - cos x tan x + sin x tan x (d) . I+ csco = seco cote + cose (e) : sin 20 cos 20 sec o sin 0 cos B 1+ cos 2.x -= cotx sin 2.x13 16. If cos A = - with A in QII and tan B = 15 8 - with B in QIII, find the exact value of each of the following without using a calculator. a) cos 2B b) sin(2.A) 17. Find all radian solutions of each equation. (a) sin (2x) =- (b) cot* x-1=0 18. Find all solution in the interval [0,27). (a) (sin x - 2)(2sin x +