6.2 Indicate whether the function is one-to-one. 16) {(-13, -20), (-10, -20), (13, -8)}

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1 Math 0 Eam Review. Evaluate the epression using the values given in the table. ) (f g)() 7 f() g() - 7 Evaluate the epression using the graphs of = f() and = g(). ) Evaluate (fg)(). 9) H() = - 7 Solve the problem. ) The surface area of a balloon is given b S(r) = πr, where r is the radius of the balloon. If the radius is increasing with time t, as the balloon is being blown up, according to the formula r(t) = t, t 0, find the surface area S as a function of the time t. Find the domain of the composite function f g. ) f() = 8 + 7; g() = + 7 ) f() = + ; g() = + 8 ) f() = - - ; g() = - ) f() = ; g() = + ) f() = - ; g() = - For the given functions f and g, find the requested composite function value. ) f() = +, g() = + ; Find (g f)(). For the given functions f and g, find the requested composite function. ) f() = +, g() = - ; Find (f g)().. Indicate whether the function is one-to-one. ) {(-, -0), (-, -0), (, -8)} Use the horizontal line test to determine whether the function is one-to-one. 7) ) f() = -, g() = + ; Find (g f)(). Decide whether the composite functions, f g and g f, are equal to. ) f() =, g() = 7) f() = +, g() = Find functions f and g so that f g = H. 8) H() = 9 + Find the inverse of the function and state its domain and range. 8) {(-, ), (-, ), (0, ), (, ), (, 7)}

2 Find the inverse. Determine whether the inverse represents a function. 9) {(, -), (, -), (0, -), (-, -)} The graph of a one-to-one function f is given. Draw the graph of the inverse function f- as a dashed line or curve. 0) f() = + ) f() = +, 0 7) f() = + 8 Find the inverse function of f. State the domain and range of f. 8) f() = Approimate the value using a calculator. Epress answer rounded to three decimal places. 9). 0).8π - ) Use the graph of the given one-to-one function to sketch the graph of the inverse function. For convenience, the graph of = is also given. ) (, ) (-, -) (-, ) (0, ) Decide whether or not the functions are inverses of each other. ) f() = ( - ), ; g() = + ) f() = ( - ), ; g() = + ) e-. Determine whether the given function is eponential or not. If it is eponential, identif the value of the base a. ) H() ) - H() 0 ) f() = +, g() = - The function f is one-to-one. Find its inverse. ) f() = +

3 Use transformations to graph the function. Determine the domain, range, and horizontal asmptote of the function. 8) f() = e ) f() = ) f() = - + 9) f() = - e Graph the function. 7) f() = ( + ) -. Solve the equation. 0) + = ) - = ) - = ) (e) e = e Solve the problem. ) The number of books in a small librar increases according to the function B = 800e 0.0t, where t is measured in ears. How man books will the librar have after ears?

4 . Change the eponential epression to an equivalent epression involving a logarithm. ) - = ) e = 7 Graph the function and its inverse on the same Cartesian plane. 9) f() = log Change the logarithmic epression to an equivalent epression involving an eponent. 7) log / 8 = - - 8) log = - 9) ln = 9 Find the eact value of the logarithmic epression. 0) log Graph the function. 0) f() = - ln( + ) ) log ) log ) log ) ln e Use a calculator to evaluate the epression. Round our answer to three decimal places ) log ) f() = log ( - ) ) log 9 + log ln - ln - - Find the domain of the function. 7) f() = log( - ) - - 8) f() = log9(0 - ) Solve the equation. ) log = ) log ( - ) =

5 ) ln 9 = ) e =. Use the properties of logarithms to find the eact value of the epression. Do not use a calculator. ) log. Solve the equation. 78) log = 79) log ( + ) = log ( - ) 80) log ( + ) = log 8 () 7) ln e 8) log ( + 0) = - log 8) log 0 log0 8) (7 - ) = 9) eln Suppose that ln = a and ln = b. Use properties of logarithms to write each logarithm in terms of a and b. 70) ln 0 Write as the sum and/or difference of logarithms. Epress powers as factors. 7) log 8 r s Solve the equation. Epress irrational answers in eact form and as a decimal rounded to decimal places. 8) = -.7 Find the amount that results from the investment. 8) $80 invested at % compounded quarterl after a period of 8 ears Find the effective rate of interest. 8).8% compounded continuousl 7) log 7 sr 7) ln ()9 + ( - 7)7 Epress as a single logarithm. 7) log b 9 + log b, > 7 8) 0.0% compounded dail Find the present value. Round to the nearest cent. 87) To get $,000 after ears at % compounded semiannuall Solve the problem. 88) What principal invested at %, compounded continuousl for ears, will ield $0? Round the answer to two decimal places. 7) log c q - log c r + log c f - log c p Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round our answer to two decimal places. 7) log ) log (/) 9 Solve the problem. Round our answer to three decimals. 89) What annual rate of interest is required to triple an investment in ears? Solve the problem. 90) How long does it take $ to triple if it is invested at 7% interest, compounded quarterl? Round our answer to the nearest tenth.

6 9).8 Conservationists tagged 0 black-nosed rabbits in a national forest in 990. In 99, the tagged 0 black-nosed rabbits in the same range. If the rabbit population follows the eponential law, how man rabbits will be in the range ears from 990? 9) Assume that the half-life of Carbon- is 700 ears. Find the age (to the nearest ear) of a wooden ae in which the amount of Carbon- is 0% of what it originall had. 9) A thermometer reading F is brought into a room with a constant temperature of 80 F. If the thermometer reads F after minutes, what will it read after being in the room for 7 minutes? Assume the cooling follows Newton's Law of Cooling: U = T + (Uo - T)ekt. (Round our answer to two decimal places.) 9) The logistic growth model 90 P(t) = represents the + 8.8e-0.t population of a bacterium in a culture tube after t hours. What was the initial amount of bacteria in the population? 9) The logistic growth model 90 P(t) = represents the population + e-0.7t of a bacterium in a culture tube after t hours. When will the amount of bacteria be 800?

7 Answer Ke Testname: 0 TEST REVIEW ) ) ) 0 ) + 8 ) ) Yes, es 7) No, no 8) f() = ; g() = 9 + 9) f() = ; g() = - 7 ) S(r(t)) = πt ) { is an real number} ) { -} ) { 0, -8} ) { -} ) {, 0} ) No 7) No 8) {(, -), (, -), (, 0), (, ), (7, )} D = {,,,, 7}; R = {-, -, 0,, } 9) {(-, ), (-, ), (-, 0), (-, -)}; a function 0) ) ) Yes (, ) (, 0) (, -) - - (-, -) - 7

8 Answer Ke Testname: 0 TEST REVIEW ) No ) Yes ) f-() = - ) f-() = -, 7) f-() = - 8, 0 8) f-() = + ; domain of f: { -}; range of f: { } - 9).78 0) 8.09 ).77 ) 0. ) Not eponential ) Eponential; a = ) domain of f: (-, ); range of f: (-, ); horizontal asmptote: = ) domain of f: (-, ); range of f:(, ) horizontal asmptote: =

9 Answer Ke Testname: 0 TEST REVIEW 7) ) ) ) {} ) {} ) {, -} ) {9, } ) 90 ) log = - ) ln 7 = - 7) = 8 9

10 Answer Ke Testname: 0 TEST REVIEW 8) = 9) e9 = 0) ) - ) 0 ) ) ) ) -. 7) (, ) 8) (-, ) 9) - - 0)

11 Answer Ke Testname: 0 TEST REVIEW ) ) {} ) {,-} e ) 9 ) ) ln 7) 8) 9) 70) a + b - 7) log 8 + log 8 r - log 8 s 7) log 7 - log 7 s - log 7 r 7) ln + ln + ln ( + ) - 7ln ( - 7) 9 7) log b 9 7) log c q f/ r/ p 7) ) ) {} 79) 80) {} 8) {} 8) {} ln 8) ln + ln 0. 8) $7.80 8).% 8).9% 87) $88.

12 Answer Ke Testname: 0 TEST REVIEW 88) $.9 89) 7.% 90).8 ears 9) 00 9) 990 ears 9) 8. F 9) 0 9).97 hours

MAC 1105 Chapter 6 (6.5 to 6.8) --Sullivan 8th Ed Name: Practice for the Exam Kincade

MAC 1105 Chapter 6 (6.5 to 6.8) --Sullivan 8th Ed Name: Practice for the Exam Kincade MAC 05 Chapter 6 (6.5 to 6.8) --Sullivan 8th Ed Name: Practice for the Eam Date: Kincade MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use the properties