Evaluate the expression using the values given in the table. 1) (f g)(6) x f(x) x g(x)

Transcription

1 M60 (Precalculus) ch5 practice test Evaluate the expression using the values given in the table. 1) (f g)(6) 1) x f(x) x g(x) For the given functions f and g, find the requested composite function value. ) f(x) = x - 6 x, g(x) = x + 9; Find (g f)(-). ) 3) f(x) = x + 3, g(x) = 3x; Find (f g)(). 3) For the given functions f and g, find the requested composite function. 4) f(x) = 4x + x + 6, g(x) = x - ; Find (g f)(x). 4) Decide whether the composite functions, f g and g f, are equal to x. 5) f(x) = 5 x - 15, g(x) = x ) 6) f(x) = x +, g(x) = 3x - 6) 3 Find the domain of the composite function f g. ) f(x) = ; g(x) = x + 4 ) x + 8 8) f(x) = 3 ; g(x) = x - 3 8) x - 6 Indicate whether the function is one-to-one. 9) {(5, ), (6, ), (, -6), (8, 5)} 9) Decide whether or not the functions are inverses of each other. 10) f(x) = 3x - 8, g(x) = x ) 11) f(x) = (x - 4), x 4; g(x) = x ) The function f is one-to-one. Find its inverse. 1) f(x) = 6x + 1) 13) f(x) = 3 x - 13) 1

2 Determine whether the given function is exponential or not. If it is exponential, identify the value of the base a. 14) 14) x H(x) Solve the equation. 15) log3 x + log3(x - 4) = 4 15) 16) + log3(x + 5) - log3 x = 4 16) 1) ( + 3x) = 1 4 1) 18) f(x) = x and g(x) = 1. Find the point of intersection of the graphs of f and g by solving f(x) = g(x). 18) 19) Find out how long it takes a $3400 investment to double if it is invested at 9% compounded 19) semiannually. Round to the nearest tenth of a year. Use the formula A = P 1 + r nt. n 0) The formula A = 83e 0.08t models the population of a particular city, in thousands, t years after When will the population of the city reach 335 thousand? 0) Find the amount that results from the investment. 1) $1,000 invested at 6% compounded quarterly after a period of 4 years 1) ) Carla has just inherited a building that is worth $50,000. The building is in a high demand area, and the value of the building is projected to increase at a rate of 5% per year for the next 4 years. How much more money will she make if she waits four years to sell the building instead of selling now? ) Find the effective rate of interest. 3) 10% compounded continuously 3) 4) 4.5% compounded monthly 4)

3 5) Which of the two rates would yield the larger amount in 1 year: 9% compounded monthly or % compounded annually? 5) Find the present value. Round to the nearest cent. 6) To get $6500 after 1 years at 13% compounded quarterly 6) ) What principal invested at 6%, compounded continuously for 3 years, will yield $1500? Round the answer to two decimal places. ) Round your answer to three decimals. 8) What annual rate of interest is required to triple an investment in 6 years? 8) 9) How long will it take for an investment to triple in value if it earns 9.5% compounded continuously? 9) 30) A culture of bacteria obeys the law of uninhibited growth. If 140,000 bacteria are present initially and there are 609,000 after 6 hours, how long will it take for the population to reach one million? 30) 31) The size P of a small herbivore population at time t (in years) obeys the function P(t) = 900e 0.13t if they have enough food and the predator population stays constant. After how many years will the population reach 00? Round to the nearest hundredth. 3) A fossilized leaf contains 6% of its normal amount of carbon 14. How old is the fossil (to the nearest year)? Use 5600 years as the half-life of carbon ) 3) 33) The half-life of carbon-14 is 500 years. Find the age of a sample in which 8% of the radioactive nuclei originally present have decayed. 33) 34) If -x = 1 4, what does 4x equal? 34) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. The graph of an exponential function is given. Match the graph to one of the following functions. 35) 35) A) f(x) = -5 -x B) f(x) = 5 x C) f(x) = -5 x D) f(x) = 5 -x 3

4 Use transformations to graph the function. Determine the domain, range, and horizontal asymptote of the function. 36) f(x) = - x ) Solve the equation. 3) x - 3 = 64 3) 38) 9 x (3 - x) = ) 39) e x - 6 = 1 e 5 x ) Change the exponential expression to an equivalent expression involving a logarithm. 40) 6 3 = 16 40) 41) e x = 15 41) Find the exact value of the logarithmic expression. 4) log1/5 65 4) Change the logarithmic expression to an equivalent expression involving an exponent. 43) logb 49 = 3 43) 44) The ph of a chemical solution is given by the formula ph = -log10[h + ], where [H + ] is the concentration of hydrogen ions in moles per liter. Find the ph if [H+] = Round to the nearest hundredth. 44) Find the domain of the function. 45) f(x) = log10 x + 8 x - 45) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. The graph of a logarithmic function is shown. Select the function which matches the graph. 46) 46) A) y = log x - B) y = log( - x) C) y = log(x - ) D) y = - log x 4

5 Solve the equation. 4) log30 (x - x) = 1 4) The loudness L(x), measured in decibels, of a sound of intensity x, measured in watts per square meter, is defined as L(x) = 10log ( x I0 ), where I 0 = 10-1 watt per square meter is the least intense sound that a human ear can detect. Determine the loudness, in decibels, of the sound. 48) A particular Boeing 4 jetliner produces noise at a loudness level of 113 decibels. Find the intensity level (round to the nearest hundredth) in watt per square meter for this noise. 48) Suppose that ln = a and ln 5 = b. Use properties of logarithms to write each logarithm in terms of a and b. 49) ln 0 49) Write as the sum and/or difference of logarithms. Express powers as factors ) log 1 q p 50) Express as a single logarithm. 51) 8ln (x - ) - 3 ln x 51) Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to two decimal places. 5) log35 5) 5

6 Answer Key Testname: CH5PRAC 1) 0 ) 5 3) 3 4) 8x + 4x + 5 5) Yes, yes 6) Yes, yes ) {x x -1} 8) {x x 3, x 39} 9) No 10) No 11) Yes 1) f-1(x) = x ) f -1 (x) = x ) Exponential; a = 15) {} 5 16) 1) {-3} 18) (log1, 1) 19).9 yr 0) 004 1) $15,.83 ) $360, ) 10.51% 4) 4.334% 5) 9% compounded monthly 6) $ ) $ ) 18.31% 9) years 30) 8.04 hours 31) 8.45 yr 3),689 33) 686 years 34) 16 35) A 6

7 Answer Key Testname: CH5PRAC 36) domain of f: (-, ); range of f: (-, 4); horizontal asymptote: y = 4 3) {3, -3} 38) {-11} 39) ) log 6 16 = 3 41) ln 15 = x 4) -4 43) b /3 = 49 44) ) (-, -8) (, ) 46) B 4) {-5, 6} 48) 0.0 watt per square meter 49) 1 (a + b) 50) 1 5 log log 1 q - log 1 p 51) ln 5).93 (x - )8 x 3