Math Eam Review Name Do the following as indicated. For the given functions f and g, find the requested function. ) f() = - 6; g() = 9 Find (f - g)(). ) ) f() = 33 + ; g() = - Find (f g)(). 3) f() = ; g() = - Find ( f g )(). - - ) f() = + ; g() = 7 + 6 Find (f + g)(). ) f() = + 9; g() = 8-3 Find (g f)(). 6) f() = 3 + 3; g() = -3 Find (f g)(). Find the inverse of the one-to-one function. 7) f() = + 9 Graph the function and its inverse on the same set of aes. 3) = log ; = Solve for. ) 7 = 9 ) (3 - ) = 6 6) 3 - = 8 8) f() = 3 + 7) log 3 = Graph the eponential function. 9) f() = + 8) log 3 = ) f() = 3 + 9) log = Determine whether the graph of the function is the graph of a one-to-one function. 0) log = 3.9 (Give eact answer) ) ) log 7 =. (Round answer to four decimal places.) ) ln =.7 (Round answer to four decimal places.) - 3) ln = 0. (Round answer to four decimal places.) -
Find the value of the logarithmic epression. ) log 00 ) 9 log 9 0 6) log 8 7) log Write the epression as sums or differences of multiples of logarithms. 8) log - 8 0) e( + ) = Solve the equation. Give an eact solution. ) 3 + 6 = ) e = 7 3) log ( - 6) = 7 ) log + log ( - 8) = 3 3 ) log ( + ) - log = 9) log 7 Epress as the logarithm of a single epression. Assume that variables represent positive numbers. 30) log 6 ( - ) - log 6 ( - ) 3) ( log a - log a ) + 3 log a z Solve. 6) log = log (3 + 8) 7) Use the formula R = log a + B to find the T intensit R on the Richter scale, given that amplitude a is micrometers, time T between waves is seconds, and B is 3. Round answer to one decimal place. Use a calculator to approimate the logarithm to four decimal places. 3) log 9 33) log 3 π 8) The amount of a radioactive substance present, in grams, at time t in months is given b the formula = 7000()-0.t. Find the number of grams present in ears. If necessar, round to three decimal places. 3) ln π3 3) ln 0.99 36) log 37) log π Solve the equation. Give an approimate solution to four decimal places. 38) 7 = 3.7 9) Calculate how much mone Lavel has after ears if he originall invested $0 at 6.6% compounded continuousl. Use A = Pert, where A is the final amount, P is the original amount deposited, r is the interest rate, and t is the number of ears. 0) The size of the raccoon population at a national park increases at the rate of.9% per ear. If the size of the current population is 7, find how man raccoons there should be in 8 ears. Use = 0 e0.09t and round to the nearest whole number. 39) 3 + 8 = 6
) Find out how long it takes a $900 investment to earn $00 interest if it is invested at 9% compounded monthl. Round to the nearest tenth of a ear. Use the formula A = P + r nt. n 67) + = 68) ( + ) 9 + ( - ) = Find the distance between the pair of points. ) (-, -7) and (, -3) 69) ( + ) 9 - ( + ) 9 = Find the midpoint of the line segment whose endpoints are given. 3) ( 3, -7 6), (8 3, - 6) Write an equation of the circle with the given center and radius. ) (9, -); 70) 6-9 = 7) ( - ) 6 - ( + ) = Solve the nonlinear sstem of equations for real solutions. 7) = - - 9 - = 8 ) (0, -); Find the center and the radius of the circle. Do not graph. 6) + + + 6 + 3 = 0 7) + - - + = 0 8) + - 8 + + 7 = 73) 7) 7) = - - = 0 = - = - + = 30 - = 3 Sketch the graph of the equation. If the graph is a parabola, find its verte. If the graph is a circle, find its center and radius. If itʹs an ellipse or hperbola, find center and values of a and b. 9) = - 60) = ( + ) - Solve. 76) + = 6 - = 6 77) The sum of the squares of two numbers is. The sum of the two numbers is 3. Find the two numbers. 6) = + + 6) = - 6 + 33 78) A rectangular holding pen for sheep is to be designed so that its perimeter is 0 meters and its area is 9 square meters. Find the dimensions of the holding pen. 63) + = 6 6) + ( + 3) = 9 6) ( - ) + ( - ) = 6 66) 6 + = 00 3
Answer Ke Testname: EXAMREVIEWFALL09 ) (f - g)() = -9 + - 6 ) (f g)() = - 63 + - 3) ( f g )() = -, where ) 8 + ) 8 + 9-3 6) -73-9 7) f-() = - 9 8) f-() = 3-9) ) ) No ) Yes 3) - - - - - - - - 6 inverse -6 function 6-6 ) 3 ) 3 6) 0 7 7) 8 8) 9 9) 0 0) 3.9 ) 0.933 ).038 3) 0.397 ) -3 ) 0 6) 0 7) 8) log ( - ) - 8 log 9) log 7 + log - log - 30) log 6 - z3 3) log a 3).7 33) -0.000 3) 3.3 3) -0.0080 36) 0.307 37).88 38) 0.696 39) -6.369 0) -0.3906 ) log log 3-6 ) ln 7 3) 7, - ) 9 ) 6) 7, - 7) 8).78 9) $38.7 0) 73 ). ears ) 3 units 3) ( 3 3, - 6 ) ) ( - 9) + ( + ) =
Answer Ke Testname: EXAMREVIEWFALL09 ) + ( + ) = 6) center (-, -3), radius = 7) center (7, ), radius = 7 8) center (, -), radius = 9) verte (0, 0) 6) verte (, ) - - - - - - - - 63) center (0, 0); radius = 60) verte (-, - ) - - - - - - - 6) center (0, -3); radius = 3-6) verte (-, -) - - - - - - - 6) center (, ); radius = - - - - -
Answer Ke Testname: EXAMREVIEWFALL09 66) 70) - - - - 67) - - - - 68) - - - - 69) - - - -