College Algebra Final Exam Review Solve the equation. 19) through (3,9) and (0, 'l 12 )-+_:4 'x 3x -4) 20)horizontal, through (3, -5) 2x+2 ^' -/ 2x 2 21) vertical, through (2, x-2 -1) Solve and write the solution set in interval notation. 3) l2x-81 =5 22)12-3xlz11 ..x672 'x-6 x+6 *2-36 23) l-8x +91 <6 ar _ 24)x2+6x-720 76.2 'x+2 x-4 v -7 25):-'x+lJ s0 6)\F+3=x-3 Find the center and radius of the circle. T).\[;+6*",12-"=+ 2Qx2*y2*8x-10y-8=0 8)x2+ 4x+20=0 27) x2 + y2 + 12x \x2+x+3=0 Graph the function. Find the vertex. za) xl:g 10)lr ' l^ logr(x + 2) + logu(x - 2) = Graph the basic function using a solid line. Graph the transformed function using a dotted line. Give the domain and range of the transformed function. 3 2e)h(x)={-x+1-2 12)Iog(x+3)=1-logx Graph the polynomial function. Find intercepts, describe end behavior, and the behavior at the zeros. 13)lnx- lt'r(x-3):ln5 t+128 f(x) = 2(x + 7)2 - 4 I 12 -11 11) - 1) : \7 30) f(x) = -3121x + 2)(x + 1) (nearest 1000th) Sketch the graph of the rational function. Identify the vertical and horizontal asymptotes. and intercepts. Find the center-radius form of the equation of ortnecrrcre' the circle. 15)center (-6,-4),radius3 15) center (4, 0), radius 7 ! ) 31)f(x):- - Graph. Find the y-intercept and the horizontal asymptote. 32) f(x) #17 - - 2y + 28=0 21)Write an equation for the line described slope- y intercept form. (if possible). 17) parallel to y + 6x = 4, through (3,4) in 18) perpendicular to 7x + 4y = 69, through (7, = [ll.'.,l - ' If f is one-to-one, find an equation for its inverse. sa)f(x) :x3-1 -5) 34) f(x) = -5x + #44 1 - 46) Find the matrix indicated when possible. l--2 *,)[_l;:]l;l Solve the problem. 35) The period of vibration P for a pendulum varies directly as the square root of the lengih L. If the period of vibration is 4.5 sec when the length is 81 inches, what is the period when L = 1.5625 inches? (nearest 1000th) 36) The volume V of a given mass of gas varies directly as the temperature T and inversely as 1 *,f -i : lt? -3;) lr 47)Letc = | -e lz | -r andD=l .FindC-4D 3 lz the pressure P. If V = 65.0 in3 when T = 100'and =20lblinZ, what is the volume when T = 160' and P = 20lblin2? (nearest 1Oth) P 37) A certain radioactive isotope has a half-life of approximately 1400 years, How many years to the nearest year would be required for a given amount of this isotope to decay lo 20% of that Evaluate the sum. 4 48) ) gz -21 k=1 5 4e) )tzi-ei i=2 amount? Find the product or quotient. Answer in standard form. 38) (e - a\Q + ei) Find the veftex, x-intercept(s), y-intercept, axis of symmetry, domain and the range, and graph each function. 50)Y=x2+2x-9 8-6i 39)'5+3i 51) Y= Solve the problem. Use these interest formulas as - e=dr*alnt t ") , necessary: +3x-9 Find the indicated composition. 52)f(x)={x.8, B(x)=-f , tr.tX*) A=Pert 40) Find the number of years for $12,600 to grow to $18,800 at 5% compounded quarterly, Round to the nearest tenth of a year. 41) Find the future value of $3933 invested years at 5% compounded quarterly -x2 for 4 42) How long will it take for $9800 to grow to $ 14,500 at an interest rate of 6.1% if the interest is compounded continuously? Round the number of years to the nearest hundredth. 53) f(x) = 7x + 14, 8(x) = 4x - 1, (f " gX*) Find all of the zeros and factor f(x) into linear factors. s+) f(x) : 6x3 + 37x2 + 32x - L5 ss)f(x) =2x3-3x2- 5x+6 Solve. Give exact solutions without using logarithms. sor p]"=zso Solve the system. 43) x+y+ z=-2 x-y+22=2 4x+y+ z:-1,'L = 14 2x2 + 4y2: 68 44)2x2 -2y2 *6:e*-s ",b.] Determine the end behavior of the function. 58) P(x) = - 6x3 + 3x2 + 8x - 2 59) P(x) =7x6 - x5 + 5x2 - Determine the intervals over which the function is 3 decreasing, increasing, and constant. 6e) Solve the problem. 60) Iill is 20 kilometers away from Joe. Both begin to walk toward each other at the same time. Jill walks at 1.5 kilometers per hour. They meet in 5 hours. How fast is Joe walking? 61) Noah and Ben are running in the Walker Street Fun Run. Noah runs al7 mph, Ben at 5 mph. If they start at the same time, how long (in minutes) will it be before they are f mile apart? 62) How much pure acid should be mixed with 9 gallons ol a507" acid solution in order to get an 80% acid solution? Compute and simplify the differen." eooti"ntl1l{-JBl, h;.0. 63) A chemist needs 120 milliliters of a 607o solution but has only 44"/o and92o/" solutions available. Find how many milliliters of each that should be mixed to get the desired solution. For the points P and Q, find the distance d(P, Q). 64) P(4, -1), Q6, -7) Decide whether the relation defines a function. 65) I(2,7), (-3, -6), (3, -4), (3,6)j 70) f(x) = 3x2 + 5x Write the expression as a sum, difference, or product of logarithms. Assume that all variables represent positive real numbers. 71) tog4 i€ 72) tog2t l-l 66) y =\Fx-o Give the domain and range of the relation. 67)y="16"-4 An equation that defines y as a function of x is given. Solve for y in terms of x, and replace y with the function notation lf, I quotient and power rules of logarithms to rewrite the expression as a single logarithm. Assume that all variables represent positive real numbers. 73) (logu q - loga r) + 6 logu p Use the product, z+1 ! bg, "n . + bs2 x4 - | bg.2* f(x). 68) 3x - 6y =/ Write out the first five terms of the sequence. ,., /3)an=n'-n