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MAC 1105 - College Algebra Final Exam 3 128 J Jonse 0 Ojed Date:_ Name: Show your work; an answer alone, even correct, will get no credit. An illegible will not be graded, so write your work neatly. Find the center and radius of the circle with the given equation: Write the equation in the standard fo 1) x2 + y2 -18% + 8y=-61 cen rad standard Find functions f and g so that fog=H. Neither f nor g can be identity functions 2) H6c) = (5 - 2x3) Express as a single logarithm. 3) log3 (5x+2) – 2 log3 (x+5) – 4log3 (3x + 1) : 7 3.42 + 3x = 15 Find the distance d(P1, P2) between the points P1 and P2. $) P1=(-1,-5); P2 = (6,-6) Find the intercepts for the graph of the equation. 1 6 x-intercepts y-intercepts granh of a one to ono uno the intercepts for the graph of the equation. 1 x2 - y2 + 5x + 6 y-intercepts x-intercepts The graph of a one-to-one function is given. Draw the graph of the inverse function f-1. For conveni 10 also given. 4- (4.4) 3 2 + + st 2 5 6 x 1 U -5 -6 -3 no -2 -1 -4 (-1, -1) 3 Graph the function f by starting with the graph of y = x3 and using transformations (shifting, comp reflection). Show the steps in the order a,b,c,d (see graphs) and write the formula for each function. 11) f(x) = - (x+1)3 + 1 y= (a) y=x3 (b) Iy 8 8 + -6 4 را • ? 6 x -6 -2 · -- . -6 - 8 (c) y = (d) y = -(x+1)3 + 1 ca S 6 T. + 2 6 X -6 T. Graph the function using ita varten, avio of symmetry, and intercepto, Show Sun WHO) 12) k) = -6 2 2 2 2 vertex: Axis of symmetry: x-intercepts: y-intercept Find the domain of the given function. Write it in the interval notation. X-3 13) h(x) = VE 7-8 Function fis one-to-one. Find the inverse f-1. 6x x-2 £-1()= 14) f(x) = Sketch the graph of the function. State the domain, find the intercepts and give the equations of asymptote *** 15) f(x) = у 10 8 6 + -10 -6 -4 of the function. State the domain, find the intercepts and give the equations of asymptote - 2x ·10 8 -10 -8 -6 -4 -? .-6 x-intercepts: y-intercep asymptote(s) horizontal asymptote: transformations to graph the function. Start with the basic function and show all steps in the order a, b, c. W each function. Write the equations of asymptotes, if any. 16) f(x) = log3 (x+2) + 1 b) y a) y = VO 67 6 2 + -6 6 -6 -2 2 4. • A -2 4 -6 --67 c) y = log3(x+2) + 1 > 6 х -6 守 2 . -6 asymptote(s) Graph the function. 17) **) - {**2 4 38*
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