College Algebra Review for Test 4

Transcription

1 College Algebra Review for Test Evaluate the epression b hand. ) a) /2 b) 27/3 c) 32/ d) 8-/3 Use positive rational eponents to rewrite the epression. 2) 2 Use radical notation to rewrite. 3) a-/2b/7 Solve the equation. ) 8q - 7 = 7 Answer the question. ) For f() = 2 - and g() = +, what is the domain of f + g? ) For f() = 2 - and g() = 2 + 3, what is the domain of f - g? ) For f() = 2 - and g() = 2 + 3, what is the domain of g/f? Evaluate as instructed. 7) Use the graph to evaluate the following: ) - 3 = 2-3 ) 3 - = ) 3/ - 9 = 0 Use translations of the graph of f() = to help sketch a graph of g. 8) g() = Evaluate as instructed. 9) Use f() = 3 + and g() = - 2 to evaluate the following: a) (f + g)(2) b) (f - g)(-3) c) (fg)(-2) d) (g/f)(2) Use the given functions to find the requested function. ) f() = 3 +, g() = 22 Find (fg)(). ) f() = 2 + 9, g() = 2 Find (f + g)(). 2) f() = 7 + 7, g() = 32 Find (g/f)(). 3) f() = 9 -, g() = - 8 Find f - g. a) (f+g)(3) b) (g-f)() c) (fg)(-2) Evaluate the function as indicated. 8) Find g(b) when g() = ) Find g( + ) when g() = ) Find (f g)(-) when f() = - - and g() = ) Find (g f)(3) when f() = and g() = -/. Find and simplif the indicated composite for the pair of functions. 22) Given f() = and g() = + 2, find (g f)(). 23) Given f() = (f g)(). - and g() = 7 3, find

2 College Algebra, Review for Test Page 2 2) Given f() = + 9 and g() = 8-3, find (f g)(). Answer the question. 2) For f() = 2 - and g() = 2 + 3, what is the domain of f g? Use the graph to determine whether the function is one-to-one. 3) 2) For f() = 2 - and g() = + 3, what is the domain of f g? What is the domain of g f? Complete numerical representations for the functions f and g are given. Evaluate the epression, if possible. 27) a) (f g)(3) b) (f g)() 8 2 f() g() - 8 Use the graph to evaluate the epression. 28) (f g)() 32) Use the table to determine if f is one-to-one. If so, use the table for f() to find a table for f-(). 33) f() 3 3-3) 9 7 f() Determine whether or not the function is one-to-one. 3) a) f() = 3 + b) f() = 32 - Find the functions f and g so that F() = (f o g) (). 29) a) F() = b) F() = ( + ) 3 + Solve. 30) The function f() = 2. converts a measurement of inches to centimeters. Find a function g that will convert an area in square inches to square centimeters. Find a smbolic representation for f-(). 3) a) f() = 8 + b) g() = + 8 c) h() = Determine i) the domain of the function, ii) the range of the function, iii) the domain of the inverse, and iv) the range of the inverse. 37) f() =

3 College Algebra, Review for Test Page 3 38) f() = 2-39) f() = + Use f() to complete the table for f-(). 0) f() = 2 + f-() -2-0 ) f() = 3 - f-() Use the table(s) to evaluate the given epression. 2) g() 8 3 a) g -() b) g -(9) Use the graph of f to sketch a graph of the inverse of f using a dashed curve. 3) Find either a linear or an eponential function that models the data in the table. ) ) ) In 99 the population of a certain cit was 0,000. Since then, the population has been growing at the rate of 3.% per ear. Is this an eample of linear or eponential growth? Find a function f that computes the population ears after 99. Find C and a so that f() = Ca satisfies the given conditions. 8) f(0) = 7 and f() = 8 9) f() = and for each unit increase in, the output is multiplied b 3. Graph the eponential function. 0) a) = b) = Use the appropriate compound interest formula to determine the final value of the given amount. ) $2,000 at % compounded quarterl for ears - 2) $900 at 8% compounded continuousl for ears ) ) The amount of a certain radioactive element remaining in a sample of 0 milligrams after ears can be described b the function A() = 0e How much is remaining after 229 ears? Round the answer to the nearest hundredth of a milligram. - Evaluate the epression b hand, if possible. ) a) log 00 b) log,000 + log 0.0 c) 2 log 0.00 d) log 0.00

4 College Algebra, Review for Test Page Simplif the epression. ) a) log 2 b) log c) log 3 27 d) log 3 8 Simplif the epression. ) a) log 29 b) log 8 c) log d) log 8 (32) e) ln (e) f) ln e 3) The Richter Scale measures the magnitude M of an earthquake. An earthquake whose seismographic reading measures millimeters 0 kilometers from the epicenter has magnitude M given b M() = log -3. Find the magnitude of an earthquake that resulted in a seismographic reading of 8,7 millimeters 0 kilometers from its epicenter. Find the domain of f and write it in interval notation. 7) f() = log ( + 9) 8) f() = log 3 (2 + ) 9) f() = ln(8 - ) 0) f() = log 3 () Solve the equation. Give an eact answer and, where appropriate, use the change of base formula to give an approimate answer rounded to decimal places. ) a) = b) = 0.98 c) 2 = 830 d) 3 = 9 e) e = 0.2 f) e- = 3 Solve the equation smbolicall. Give an eact answer and, where appropriate, also give a decimal approimation rounded to decimal places. 2) a) log 8 = b) log 2 = 2 c) log = -3 d) log 3 =. e) ln - 8 = 3 f) 7 ln 9 = 3 g) log 8 = 8.7 h) log (3 - ) =

5 Answer Ke Testname: CAREVIEW_F ) a) b) 3 c) d) 2) 2/ 3) ) 7 ) 3 ) -7 7) 8 8) 7 b a ) a) 8 b) -7 c) 2 d) - ) ) ) ) + 2 ) - ) All real numbers ) -8 or 8 7) a) 0 b) - c) undefined d) 8) b - b - 9) ) -7 2) 2 2-2) All real numbers 2) a) -3 b) 27) a) 0 b) 28) 3 29) Answers ma var. One possible answer is: a) f() = /, g() = + b) f() = 3, g() = + 30) g() =.2 3) Yes 32) No 33) Not a one-to-one function 3) f() 9 7 3) a) Yes b) No 3) a) f-() = - 8 b) g-() = - + c) h-() = ) f(): D is all real numbers, R is all real numbers; f-(): D is all real numbers, R is all real numbers 38) f(): D = 2, R = 0 ; f-(): D = 0, R = 2 39) f(): D = -, R = 0 ; f-(): D = 0, R = ) f-() ) f-() ) a) -3 b) 0 2) - 22) ) 7-2

6 Answer Ke Testname: CAREVIEW_F 3) 0) a) ) b) ) f() = 7(3) ) f() = ) Eponential; f() = 0,000(.03) 8) C = 7, a = f() = 7() 9) C = 8, a = 3 ) $,2.28 2) $ ).2 milligrams ) a) 3 b) 2 c) - d) - 3 ) a) b) 0 c) 2 d) - ) a) b) -2 c) -3 d) 3 e) f) 7) (-9, ) 8) - 2, 9) (-, 8) 0) (-, 0) (0, )

7 Answer Ke Testname: CAREVIEW_F ) a) = - b) = log c) = log d) = log e) = ln f) = -ln ) a) = 32,78 b) = c) = d) = 3.,.92 e) = e/,.27 f) = 9 e,.90 g) = 8.7, 2,8,0.2 8 h) = ) 7.8