The wage gap is used to compare the status of women's earnings relative to men's. The

In Exercises 1- 10, determine whether em;/1 relatlon is a ftmclion. Give the domain and range for each re/atiou. 1(1. 2). (3. 4). (5, 5)1

In Exercises 1- 10, determine whether em;/1 relatlon is a ftmclion. Give the domain and range for each re/atiou. [(4, 5), (6. 7), (8,8)1

In Exercises 1- 10, determine whether em;/1 relatlon is a ftmclion. Give the domain and range for each re/atiou. 1(3. 4). (3. 5}. (4, 4), (4. 5)1

In Exercises 1- 10, determine whether em;/1 relatlon is a ftmclion. Give the domain and range for each re/atiou. [(5. 6). (5, 7). (6. 6). (6. 7)}

In Exercises 1- 10, determine whether em;/1 relatlon is a ftmclion. Give the domain and range for each re/atiou. ((3. -2). (5. - 2). (7. 1). (4. 9)}

In Exercises 1- 10, determine whether em;/1 relatlon is a ftmclion. Give the domain and range for each re/atiou. ((10.4).(-2.4).{- 1.1). (5.6)}

In Exercises 1- 10, determine whether em;/1 relatlon is a ftmclion. Give the domain and range for each re/atiou. ((-3. -J). (- 2, - 2). (- 1. - I). (0. 0)1

In Exercises 1- 10, determine whether em;/1 relatlon is a ftmclion. Give the domain and range for each re/atiou. [(-7. -7). (- 5. - 5). (- 3, - 3), (0. O)J

In Exercises 1- 10, determine whether em;/1 relatlon is a ftmclion. Give the domain and range for each re/atiou. [(1.4).(1.5).(1,6)1

In Exercises 1- 10, determine whether em;/1 relatlon is a ftmclion. Give the domain and range for each re/atiou. 1(4.1). (5. 1),(6, 1)1

In Exercises 11-26. determine whether i!ilL'h efJttation defines y as a function of .r. X+ y - 16

In Exercises 11-26. determine whether i!ilL'h efJttation defines y as a function of .r. X + )' - 25

In Exercises 11-26. determine whether i!ilL'h efJttation defines y as a function of .r. x' - )' - 16

In Exercises 11-26. determine whether i!ilL'h efJttation defines y as a function of .r. x> - )' - 25

In Exercises 11-26. determine whether i!ilL'h efJttation defines y as a function of .r. x> - r' - 16

In Exercises 11-26. determine whether i!ilL'h efJttation defines y as a function of .r. x> - ,. - 25

In Exercises 11-26. determine whether i!ilL'h efJttation defines y as a function of .r. X - y'

In Exercises 11-26. determine whether i!ilL'h efJttation defines y as a function of .r. -l.r - i

In Exercises 11-26. determine whether i!ilL'h efJttation defines y as a function of .r. ) - Yx + 4

In Exercises 11-26. determine whether i!ilL'h efJttation defines y as a function of .r. -~

In Exercises 11-26. determine whether i!ilL'h efJttation defines y as a function of .r. X+ l - 8

In Exercises 11-26. determine whether i!ilL'h efJttation defines y as a function of .r. X+)~ 27

In Exercises 11-26. determine whether i!ilL'h efJttation defines y as a function of .r. xy+2.v -l

In Exercises 11-26. determine whether i!ilL'h efJttation defines y as a function of .r. xy- 5y - I

In Exercises 11-26. determine whether i!ilL'h efJttation defines y as a function of .r. J.rj - y - 2

In Exercises 11-26. determine whether i!ilL'h efJttation defines y as a function of .r. J.rj - y - 5

In Exercises 27-38. evaluate each function at Jhe given values of the independl"nl "'ariable and simplify. /(X) - .IX + 5 a. j1.6) b. j{x + I) c. jl.- x)

In Exercises 27-38. evaluate each function at Jhe given values of the independl"nl "'ariable and simplify. Jl.r) - 3x T 7 a. j1.4) b. j(x + I) c. f(- .r)

In Exercises 27-38. evaluate each function at Jhe given values of the independl"nl "'ariable and simplify. g(.r) - x' T 2r - 3 a. g(-1) b. g(x + 5) c. g (-x)

In Exercises 27-38. evaluate each function at Jhe given values of the independl"nl "'ariable and simplify. g(x) - ,IJ - IO.r - 3 " g(- 1) b. g(x + 2) c. g(- x)

In Exercises 27-38. evaluate each function at Jhe given values of the independl"nl "'ariable and simplify. /i(x) - .r' - x' + 1 11(2) c. lr(-x) b. lr(-1) d. lr(3a)

In Exercises 27-38. evaluate each function at Jhe given values of the independl"nl "'ariable and simplify. h(.r) - .r' - X + I a. lr(3) c. h(-.r) b. h(- 2) d. h(3o)

In Exercises 27-38. evaluate each function at Jhe given values of the independl"nl "'ariable and simplify. j{r) - vT"+'6 + 3 . j{-6) b. /(10) c. f(x - 6)

In Exercises 27-38. evaluate each function at Jhe given values of the independl"nl "'ariable and simplify. {r) - ~ - 6 " /1 16) b. /(- 24) c. /(25 - 2.r)

In Exercises 27-38. evaluate each function at Jhe given values of the independl"nl "'ariable and simplify. Jlx) - -;;- a. /(2) b. /(- 2) c. /(- .r)

In Exercises 27-38. evaluate each function at Jhe given values of the independl"nl "'ariable and simplify. {.r) - ---;;- a. /{2) b. j{- 2) c. jl.- .r)

In Exercises 27-38. evaluate each function at Jhe given values of the independl"nl "'ariable and simplify. j{x) - j;j " /{6) b. f(-6) c. f(rl)

In Exercises 27-38. evaluate each function at Jhe given values of the independl"nl "'ariable and simplify. f(.r - , XT:> /(5) b. j{- 5) c. f(- 9 - x)

In Exercises 39-50. graph lhe given functions, f and g. in the sam~ rtctangular coordinaJe system. S~ll imcgcnfor :c. starting -ith -2 and ending with 2. Once you ha1~ obtained your graplas. drn:ri~ hDMIh~ graph of g is related lo 1h~ graph of f. {.<) - x,g(x) - x - 3

In Exercises 39-50. graph lhe given functions, f and g. in the sam~ rtctangular coordinaJe system. S~ll imcgcnfor :c. starting -ith -2 and ending with 2. Once you ha1~ obtained your graplas. drn:ri~ hDMIh~ graph of g is related lo 1h~ graph of f. f(.r) - x,g(x) - x - 4

In Exercises 39-50. graph lhe given functions, f and g. in the sam~ rtctangular coordinaJe system. S~ll imcgcnfor :c. starting -ith -2 and ending with 2. Once you ha1~ obtained your graplas. drn:ri~ hDMIh~ graph of g is related lo 1h~ graph of f. J(.<) - -2.r,g(.r) - - 2r- I

In Exercises 39-50. graph lhe given functions, f and g. in the sam~ rtctangular coordinaJe system. S~ll imcgcnfor :c. starting -ith -2 and ending with 2. Once you ha1~ obtained your graplas. drn:ri~ hDMIh~ graph of g is related lo 1h~ graph of f. Jl.rl - - 2.r.g(.r) - - 2r + 3

In Exercises 39-50. graph lhe given functions, f and g. in the sam~ rtctangular coordinaJe system. S~ll imcgcnfor :c. starting -ith -2 and ending with 2. Once you ha1~ obtained your graplas. drn:ri~ hDMIh~ graph of g is related lo 1h~ graph of f. {.r) - .-.', g(x) - .-.' + 1

In Exercises 39-50. graph lhe given functions, f and g. in the sam~ rtctangular coordinaJe system. S~ll imcgcnfor :c. starting -ith -2 and ending with 2. Once you ha1~ obtained your graplas. drn:ri~ hDMIh~ graph of g is related lo 1h~ graph of f. f(.r} - xl,g(x) - x' - 2

In Exercises 39-50. graph lhe given functions, f and g. in the sam~ rtctangular coordinaJe system. S~ll imcgcnfor :c. starting -ith -2 and ending with 2. Once you ha1~ obtained your graplas. drn:ri~ hDMIh~ graph of g is related lo 1h~ graph of f. jl..r) - J.rJ. g(x) - Jxl - 2

In Exercises 39-50. graph lhe given functions, f and g. in the sam~ rtctangular coordinaJe system. S~ll imcgcnfor :c. starting -ith -2 and ending with 2. Once you ha1~ obtained your graplas. drn:ri~ hDMIh~ graph of g is related lo 1h~ graph of f. j{.t) - J.rJ.g(x) - JxJ + I

In Exercises 39-50. graph lhe given functions, f and g. in the sam~ rtctangular coordinaJe system. S~ll imcgcnfor :c. starting -ith -2 and ending with 2. Once you ha1~ obtained your graplas. drn:ri~ hDMIh~ graph of g is related lo 1h~ graph of f. {.r) - xl, g(x) - x' + 2

In Exercises 39-50. graph lhe given functions, f and g. in the sam~ rtctangular coordinaJe system. S~ll imcgcnfor :c. starting -ith -2 and ending with 2. Once you ha1~ obtained your graplas. drn:ri~ hDMIh~ graph of g is related lo 1h~ graph of f. j{x) - . g(x) - x' - I

In Exercises 39-50. graph lhe given functions, f and g. in the sam~ rtctangular coordinaJe system. S~ll imcgcnfor :c. starting -ith -2 and ending with 2. Once you ha1~ obtained your graplas. drn:ri~ hDMIh~ graph of g is related lo 1h~ graph of f. f(x) - 3, g(.r) - 5

In Exercises 39-50. graph lhe given functions, f and g. in the sam~ rtctangular coordinaJe system. S~ll imcgcnfor :c. starting -ith -2 and ending with 2. Once you ha1~ obtained your graplas. drn:ri~ hDMIh~ graph of g is related lo 1h~ graph of f. fl..<) - - l.g(.r) - 4

In Exercises 51-54. graph the give11 squart root functions. f and g. in tire :rame roctangular coordinate syJtem. Use the integer "aluts of x given to the right of each function to obtain ordered pain. Btt:ause only nonne-gati1e mmr~rs ha~e square roou that a~ rralmtmbtrs. bt sure thal eoch graph appn~n on(l' for ''alues of x tllat cause the expression1mder the radial/ sign to be greater than or equal to :.ero. Ona you ha1e obta;ned your graphs.. d.scrib< hoM' the graph of g is relar.d lo lh~ graph of f. j{x) - VX (.r - 0. I. 4. 9) a nd g(x) - VX - I (.r - 0, I. 4. 9)

In Exercises 51-54. graph the give11 squart root functions. f and g. in tire :rame roctangular coordinate syJtem. Use the integer "aluts of x given to the right of each function to obtain ordered pain. Btt:ause only nonne-gati1e mmr~rs ha~e square roou that a~ rralmtmbtrs. bt sure thal eoch graph appn~n on(l' for ''alues of x tllat cause the expression1mder the radial/ sign to be greater than or equal to :.ero. Ona you ha1e obta;ned your graphs.. d.scrib< hoM' the graph of g is relar.d lo lh~ graph of f. (.r) - VX (x - 0, 1,4. 9) and g(.r) - v; + 2 (.r - 0.1.4. 9)

In Exercises 51-54. graph the give11 squart root functions. f and g. in tire :rame roctangular coordinate syJtem. Use the integer "aluts of x given to the right of each function to obtain ordered pain. Btt:ause only nonne-gati1e mmr~rs ha~e square roou that a~ rralmtmbtrs. bt sure thal eoch graph appn~n on(l' for ''alues of x tllat cause the expression1mder the radial/ sign to be greater than or equal to :.ero. Ona you ha1e obta;ned your graphs.. d.scrib< hoM' the graph of g is relar.d lo lh~ graph of f. j{x) - VX (x - 0. I. 4. 9) and g(.<) - 'v"7'== (.r - 1.2. 5. 10)

In Exercises 51-54. graph the give11 squart root functions. f and g. in tire :rame roctangular coordinate syJtem. Use the integer "aluts of x given to the right of each function to obtain ordered pain. Btt:ause only nonne-gati1e mmr~rs ha~e square roou that a~ rralmtmbtrs. bt sure thal eoch graph appn~n on(l' for ''alues of x tllat cause the expression1mder the radial/ sign to be greater than or equal to :.ero. Ona you ha1e obta;ned your graphs.. d.scrib< hoM' the graph of g is relar.d lo lh~ graph of f. {x) - VX tr - 0. I. 4. 9) and g(.t) - Vx - 2 (.r - - 2.-1.2,7}

In Exercises 55-64, use-the 1enicaf line ttst to identify graphs in wlrich y is a ~tnction of x. J'

In Exercises 55-64, use-the 1enicaf line ttst to identify graphs in wlrich y is a ~tnction of x. J'

In Exercises 55-64, use-the 1enicaf line ttst to identify graphs in wlrich y is a ~tnction of x. y X

In Exercises 55-64, use-the 1enicaf line ttst to identify graphs in wlrich y is a ~tnction of x. y X

In Exercises 55-64, use-the 1enicaf line ttst to identify graphs in wlrich y is a ~tnction of x. y X

In Exercises 55-64, use-the 1enicaf line ttst to identify graphs in wlrich y is a ~tnction of x. y X

In Exercises 55-64, use-the 1enicaf line ttst to identify graphs in wlrich y is a ~tnction of x. y

In Exercises 55-64, use-the 1enicaf line ttst to identify graphs in wlrich y is a ~tnction of x. y

In Exercises 55-64, use-the 1enicaf line ttst to identify graphs in wlrich y is a ~tnction of x. y

In Exercises 55-64, use-the 1enicaf line ttst to identify graphs in wlrich y is a ~tnction of x. y

In Exercises 65- 70, use the graph off to find each indic.ated fum:tion value. y y- ftxl '--4-<:-- -:12:-l-1+\--:!2:-l--!4-) -X -2 -3 -4 f(-2)

In Exercises 65- 70, use the graph off to find each indic.ated fum:tion value. y y- ftxl '--4-<:-- -:12:-l-1+\--:!2:-l--!4-) -X -2 -3 -4 f(2)

In Exercises 65- 70, use the graph off to find each indic.ated fum:tion value. y y- ftxl '--4-<:-- -:12:-l-1+\--:!2:-l--!4-) -X -2 -3 -4 f{4)

In Exercises 65- 70, use the graph off to find each indic.ated fum:tion value. y y- ftxl '--4-<:-- -:12:-l-1+\--:!2:-l--!4-) -X -2 -3 -4 f(-4)

In Exercises 65- 70, use the graph off to find each indic.ated fum:tion value. y y- ftxl '--4-<:-- -:12:-l-1+\--:!2:-l--!4-) -X -2 -3 -4 f(-3)

In Exercises 65- 70, use the graph off to find each indic.ated fum:tion value. y y- ftxl '--4-<:-- -:12:-l-1+\--:!2:-l--!4-) -X -2 -3 -4 f(-1)

Use the graph of g to solve Exercises 71-76. y y - glx) Find g(- 4).

Use the graph of g to solve Exercises 71-76. y y - glx) Find g(2).

Use the graph of g to solve Exercises 71-76. y y - glx) Find g(- 10).

Use the graph of g to solve Exercises 71-76. y y - glx) Find g(IO).

Use the graph of g to solve Exercises 71-76. y y - glx) For what value of x is g(x) - I'!

Use the graph of g to solve Exercises 71-76. y y - glx) N>r what value of x is g(.t) --I?

In Exercises 77-92, use the graph to determine a. the June/ion's domain; b. the function :r range; c. the x-interupts, if any; d. the y.intercept, if any; and e. the missing function values, indicated by question marks, below each graph. y 4 3 2 .v -Jl.<l 1 J 4 1(-2) - ? /(2)- ?

In Exercises 77-92, use the graph to determine a. the June/ion's domain; b. the function :r range; c. the x-interupts, if any; d. the y.intercept, if any; and e. the missing function values, indicated by question marks, below each graph. y !H)- ? !(2) - ?

In Exercises 77-92, use the graph to determine a. the June/ion's domain; b. the function :r range; c. the x-interupts, if any; d. the y.intercept, if any; and e. the missing function values, indicated by question marks, below each graph. y J(- 1)- ? /(3)- ?

In Exercises 77-92, use the graph to determine a. the June/ion's domain; b. the function :r range; c. the x-interupts, if any; d. the y.intercept, if any; and e. the missing function values, indicated by question marks, below each graph. )' -3 -4 f(-4) - ? !(3)- ?

In Exercises 77-92, use the graph to determine a. the June/ion's domain; b. the function :r range; c. the x-interupts, if any; d. the y.intercept, if any; and e. the missing function values, indicated by question marks, below each graph. y 5 4 3 2 X -:!--:t"-J-t-~Lr-j-;_- X -3-2-lt -2 -3 / (3) - ?

In Exercises 77-92, use the graph to determine a. the June/ion's domain; b. the function :r range; c. the x-interupts, if any; d. the y.intercept, if any; and e. the missing function values, indicated by question marks, below each graph. y -4 J(-4)- ?

In Exercises 77-92, use the graph to determine a. the June/ion's domain; b. the function :r range; c. the x-interupts, if any; d. the y.intercept, if any; and e. the missing function values, indicated by question marks, below each graph. y -2 -3 -4 /(4)- ?

In Exercises 77-92, use the graph to determine a. the June/ion's domain; b. the function :r range; c. the x-interupts, if any; d. the y.intercept, if any; and e. the missing function values, indicated by question marks, below each graph. v 4 )'- Jl.<l /(3)- 7

In Exercises 77-92, use the graph to determine a. the June/ion's domain; b. the function :r range; c. the x-interupts, if any; d. the y.intercept, if any; and e. the missing function values, indicated by question marks, below each graph. ' -:t-r~~~~~~x -3-2- l l -2 -3 / (- 1)- ?

In Exercises 77-92, use the graph to determine a. the June/ion's domain; b. the function :r range; c. the x-interupts, if any; d. the y.intercept, if any; and e. the missing function values, indicated by question marks, below each graph. /(-2)- ?

In Exercises 77-92, use the graph to determine a. the June/ion's domain; b. the function :r range; c. the x-interupts, if any; d. the y.intercept, if any; and e. the missing function values, indicated by question marks, below each graph. y 4 3 2 -3 -4 1(-4)- ? /( ?

In Exercises 77-92, use the graph to determine a. the June/ion's domain; b. the function :r range; c. the x-interupts, if any; d. the y.intercept, if any; and e. the missing function values, indicated by question marks, below each graph. y I -2 -3 -4 1(-2) - ? l(l)- ?

In Exercises 77-92, use the graph to determine a. the June/ion's domain; b. the function :r range; c. the x-interupts, if any; d. the y.intercept, if any; and e. the missing function values, indicated by question marks, below each graph. y /( ?

In Exercises 77-92, use the graph to determine a. the June/ion's domain; b. the function :r range; c. the x-interupts, if any; d. the y.intercept, if any; and e. the missing function values, indicated by question marks, below each graph. c .. htl ,~ tN oppl _lol uhM 'ftrtictl _ fi-... r 4ll 2 l ' - ' -2 : : y - / 1.<) 0 ~fi ti4u, ttaph -4 uttt lt~ttht t1tt x-uit

In Exercises 77-92, use the graph to determine a. the June/ion's domain; b. the function :r range; c. the x-interupts, if any; d. the y.intercept, if any; and e. the missing function values, indicated by question marks, below each graph. y - Jlx) 2 I 4-3-2-Li I 2 3 4 2 -3 -4

In Exercises 77-92, use the graph to determine a. the June/ion's domain; b. the function :r range; c. the x-interupts, if any; d. the y.intercept, if any; and e. the missing function values, indicated by question marks, below each graph. y 4 3 2 -4-3-2-11 2 3 4 -2 y - Jlx) I 1(-5) /(~) ?

In Exercises 93-94.1.t If!) - x' - x - 4 and g(x) - 3x - 5. Find g(l) and f(g(l@

In Exercises 93-94.1.t If!) - x' - x - 4 and g(x) - 3x - 5. Find g(- 1) and f(g(- 1)).

In Exercises 95-96.1et .fi!nd g be defined by thc following /able: X Jl.:r) r(:rl - 2 6 0 - I 3 ~ 0 - I I - 4 -3 2 0 -6 Find V'j(- 1) - flO) - (g(2)f + ft-2) + g(2)g(- l).

In Exercises 95-96.1et .fi!nd g be defined by thc following /able: X Jl.:r) r(:rl - 2 6 0 - I 3 ~ 0 - I I - 4 -3 2 0 -7 Find IJit) - JIO)I - [g(l))' + g(l) + j{-t) g(2).

In Exercises 97-98.find fl- x) - f(:r) for the given funcrion f. Then .\implify the expression. (.r) - x1 + x - 5

In Exercises 97-98.find fl- x) - f(:r) for the given funcrion f. Then .\implify the expression. (.r) - x1 + x - 5

The bar graph shmt'S minin111m /~gal ag~ for sa and marriage in fi\'t! stlecud countries. Use this information to solve Exercises 99-100. (We did not include data for the United States bocause t!Je legal age of sexual com~cnt \aries according to state law. Fttrt!Jermore, women are allowed to marry younger than men: 16 for women and 18 for men.) 19 18 17 16 IS 14 13 12 12 MilliiiiiUD Lqol Ages f0< S.x IUid M:urillge, lor Heten> a. \Vrite a set of five ordered p3irs in which countries correspond to the minimum legal age of sexual consent. Each ordered pair should be in the fonn (country, minimum legal ngc of sexual consent). b. Is the re lation in part (a) o function? Explain your answer. c. Write. a set of five ordered pairs in which the minimum legal age of sexuaJ consent corresponds to a country. Each ordered pair should be in the loon (minimum legal age o( sexual consent. counb)1). d. Is I he relation in part (c) function?

The bar graph shmt'S minin111m /~gal ag~ for sa and marriage in fi\'t! stlecud countries. Use this information to solve Exercises 99-100. (We did not include data for the United States bocause t!Je legal age of sexual com~cnt \aries according to state law. Fttrt!Jermore, women are allowed to marry younger than men: 16 for women and 18 for men.) 19 18 17 16 IS 14 13 12 12 MilliiiiiUD Lqol Ages f0< S.x IUid M:urillge, lor Heten> a. Write a set of five ordered pa irs in which countries correspond to the minimum legal age of marriage with parental consent Each ordered pair shouJd be in the fom1 (country, minimum le.gat age of marriage ''~th parental consent). b. Is the relation in part (a) a function? Explain your answer. c. Write a set of five ordered pairs in which the minimum legal age of marriage \\~th parenta l consent oorrc.'liponds to a c.ountry. Each ordered pair should be in the form (minimum legal age of marriage wilh parentaJ consent, country). d. Is the relation in part (c) a function?

The bar graph shoks your chances of surviving 10 various age-s once you reach 60. Chances or 60-Year-Oids Su..,hing to Various Ages 90% B6 75% 60% 45% 30% 15% Age Souree: National Center for Health Statistics Section 2.1 Basics of Functions and Their Graphs 227 c. Write a set of five ordered pairs in which the minimum legal age of marriage \\~th parenta l consent oorrc.'liponds to a c.ountry. Each ordered pair should be in the form (minimum legal age of marriage wilh parentaJ consent, country). d. Is the relation in part (c) a function? The functions f(.t) - - 2.9x + 286 and g(x) - O.Olx2 - 4.9x + 370 model the chance, as a percelll, that a 60-year-old will survi11e to age x. Use this infonuationto solve Exercises 101-102. a. Find and interpret !(70). b. Find and interpret g(70). c. Which function serves as a bette r model for the chance o f su vh~ng to age 70?

The bar graph shoks your chances of surviving 10 various age-s once you reach 60. Chances or 60-Year-Oids Su..,hing to Various Ages 90% B6 75% 60% 45% 30% 15% Age Souree: National Center for Health Statistics Section 2.1 Basics of Functions and Their Graphs 227 c. Write a set of five ordered pairs in which the minimum legal age of marriage \\~th parenta l consent oorrc.'liponds to a c.ountry. Each ordered pair should be in the form (minimum legal age of marriage wilh parentaJ consent, country). d. Is the relation in part (c) a function? The functions f(.t) - - 2.9x + 286 and g(x) - O.Olx2 - 4.9x + 370 model the chance, as a percelll, that a 60-year-old will survi11e to age x. Use this infonuationto solve Exercises 101-102. a. Find and interpret f(90). b. Find and interpret g(90). c. Which function serves as a bette r model for the chance of surviving to age 90?

The wage gap is used to compare the status of women's earnings relative to men's. The wage gap is expressed as a percetll and is c.alcu/ated by dividing the median, or midtllemost, annual earnings for women by the median annual earnings for men. The bar graph shows the wage gap for selected years from /980 through 2010. Median Women's Earnings as a Percentage or Median Men's Earning< on the United States 83% 76% Year Source: Bureau of Labor Statistics 85 so 75 70 55 The Graph or a l'unction Modeling the Data Gjx) - - O.Olt' +x +60 1-~--:':,...--}}5,.--,!20::--,;25 --;301::- X Years after 1980 The function G(x) - - O.Ol.t2 + x + 60 models the wage gap, as a percent. x years after 1980. The graph of fimction G is shown /o the right of the actual data. Use this information lo solre Exercises 103-704. . Find and interpret G(30). Identify this infonnation as a point on the graph of the function. b. Does G(30) ov~stimate or underestimate the actual data shown by theba;raph? By how much?

The wage gap is used to compare the status of women's earnings relative to men's. The wage gap is expressed as a percetll and is c.alcu/ated by dividing the median, or midtllemost, annual earnings for women by the median annual earnings for men. The bar graph shows the wage gap for selected years from /980 through 2010. Median Women's Earnings as a Percentage or Median Men's Earning< on the United States 83% 76% Year Source: Bureau of Labor Statistics 85 so 75 70 55 The Graph or a l'unction Modeling the Data Gjx) - - O.Olt' +x +60 1-~--:':,...--}}5,.--,!20::--,;25 --;301::- X Years after 1980 The function G(x) - - O.Ol.t2 + x + 60 models the wage gap, as a percent. x years after 1980. The graph of fimction G is shown /o the right of the actual data. Use this information lo solre Exercises 103-704. a. Find and interpret G(JO). Identify this information as a point on the graph of the function. b. Does G(JO) overestimate or underestimate the actual data shown by the bar graph? By how much?

In Exercises 105-108, you wilf be developing fim<'Jions Jhat model given conditions. A company that manufactures bicycles has a fixed cost of SHJO,OOO. fl costs SJOO to produce each bicycle. The tota l cost for the company is the sum of its fixed cost and variable costs. \\'rite the total oost, C, as a function of the numbe r of bicycles produced. x. Then find and interpret C(90).

In Exercises 105-108, you wilf be developing fim<'Jions Jhat model given conditions. A car was purchased for S22.500. The value of the car decreased by $3200 per year for the first six years. Write a function that describes the value of the car, V, a fte r x years, where 0 s x s 6. ll1en find and interpret V(3).

In Exercises 105-108, you wilf be developing fim<'Jions Jhat model given conditions. You commute to work a dista nce o f 40 miles and return on the same route at the end of the day. Your average rate on the return trip is 30 miles per hour faster than your average rate on the outgoing trip. Write the total time, T. in hours, devoted to your outgoing and return trips as a function of your rate on the outgoing trip. x. Then find and inte rpre t T(30). Hint: 1 d Dista nce ll aveled tme travele - Rate of lra\iel

In Exercises 105-108, you wilf be developing fim<'Jions Jhat model given conditions. A chemist working on a flu vaccine needs to mix a 10% sodium.iodine solution \\ th a 60% sodium. iodine solution to obtain a 50-milliliter mixture. Write the amount of sodium iodine in the mixture, S, in milliliters, as a function of the number o f milliliters of the 10% solution used, x. Then find and interpret 5(30).

What is a relation? Describe what is meant by its domain and its range.

Explain how to determine whether a relation is a function. What is a function?

How do you determine if an equation in x and y defines y as a function of x?

Does f(x) mean f times x when referring to a function f? If not, what does f(x) mean? Provide an example with your explana tion.

What is the graph of a function?

Explain how the vertical line test is used to determine whether a graph represents a function.

Explain how to identify the domain and range of a function from its graph.

For people filing a single return, federal income tax is a function of adjusted gross income because for each value of adjusted gross income there is a specific tax to be paid. By contrast the price o f a house is not a function of the lot size on which the house sits because houses on same-sized lots can sell for many different prices. a. Describe an everyday situation between variables that is a function. b. Describe an everyday situation between variables that is not a function.

Use a graphing utility to verify any five pairs of graphs that you drew by hand in Exercises 39-54.

In Exercises 118--121, determine whethereach stafemelll makes sense or does not make sense, and explain your reasoning. My body temperature is a function of the rime of day.

In Exercises 118--121, determine whethereach stafemelll makes sense or does not make sense, and explain your reasoning. Using f(x) - 3.t + 2. I found [(50) by a pplying the distributive property to (1r + 2)50.

In Exercises 118--121, determine whethereach stafemelll makes sense or does not make sense, and explain your reasoning. I graphed a function shO\\~ng how paid vacation days de.pe nd on the number o f years a person works for a company.llte domain \\'as thenumberof paid vacation days.

In Exercises 118--121, determine whethereach stafemelll makes sense or does not make sense, and explain your reasoning. I graphed a function shm\~ng how the average number of annual physician visits depends on a person's age. The domain was t.he average number of annual physician \~sits.

Use the graph off to determine whether eacll statement in Exercises 122-125 is true or false. The domain off is (- 4, - I) U (- 1, 4).

Use the graph off to determine whether eacll statement in Exercises 122-125 is true or false. The range off is (- 2, 2).

Use the graph off to determine whether eacll statement in Exercises 122-125 is true or false. [(- 1) - /(4) - 2

Use the graph off to determine whether eacll statement in Exercises 122-125 is true or false. /(0) - 2.1

If f(x) - 3x + 7, find f(a + h) - [(a)

Give an example of a relation with the following characteristics: The relation is a function conta ining two ordered pairs. Reversing the components in each ordered pair results in a relation that is not a function.

If f(x + y) - f(x) + f(y) and /(I) - 3, find [(2),[(3). and [(4). Is f(x + y) - f(x) + f(y) for a ll functions?

Exercises 129-131 will help you prepare for tire material w1ered in the next section. l11e function C(t) - 20 + 0.40 (1 - 60) describes the monthly cost, C(t), in dollars, for a cellphone plan for 1 calling minutes, where 1 > 60. Find and interpret C(IOO).

Exercises 129-131 will help you prepare for tire material w1ered in the next section. Use point plotting to graph f(x) - x + 2 if x s I.

Exercises 129-131 will help you prepare for tire material w1ered in the next section. Simplify:2(x +It)'+ 3(x +It) + 5 - (2.\2 + 3x + 5).