MATH 111 CHAPTER 2 (sec )

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1 MATH CHAPTER (sec -0) Terms to know: function, te domain and range of te function, vertical line test, even and odd functions, rational power function, vertical and orizontal sifts of a function, reflection in te -ais, reflection in te y-ais, vertical stretcing and compressions of a function, constant function, linear function, point-slope equation of a line, slope-intercept equation of a line, slope of a line, parallel and perpendicular lines, quadratic function, ais of symmetry, verte, minimum/maimum value, increasing/decreasing, standard (verte) form of a quadratic function, piece-wise defined function, continuous and discontinuous function, absolute value function, aritmetic combinations of functions, function composition, inverse function, one-to-one function, orizontal line test, difference quotient, properties of inverse functions, optimization problem Be able to evaluate functions and simplify teir result (sec ) Be able to determine domain and range of te function (sec ) Know and be able to use vertical and orizontal sifts, vertical stretcing and compressions, and reflections to grap functions (sec ) 5 Know te basic sapes, domain and range, and sketc te grap of oter common functions in te mn / form y (sec ) 6 Be able to determine if a given function is even, odd or neiter even nor odd (sec ) 7 Be able to find te slope-intercept equation, and point-slope equation of a line (sec ) 8 Be able to find te equation of te line tat passes troug te point and parallel or (and) perpendicular to te given line (sec ) 9 Know te applications of te linear functions (sec ) 0 Be able to use te completion of squares tecnique to rewrite quadratic function in te verte form f ( ) a( ) + k (sec ) Be able to find te - and y-intercepts, ais of symmetry, verte, minimum/maimum value, increasing/decreasing intervals, domain and range and sketc te grap of te quadratic function (sec ) Be able to use te quadratic formula to factor and solve te quadratic equation (sec ) Know te applications of quadratic functions (sec ) Be able to determine a quadratic equation from te given grap of a quadratic function (sec ) 5 Be able to evaluate, grap, and find te domain and range of a piece-wise defined and an absolute value functions (sec 5) 6 Know te aritmetic combinations of functions, be able to find tem, and give te domain for eac combination (sec 6) 7 Be able to find composition of two and tree functions and give te domain for eac composition (sec 6) 8 Be able to write te function as te composition of few functions (sec 6) 9 Be able to find an inverse function (sec 8) 0 Be able to find te domain and range of an inverse function (sec 8) Be able to write an equation of te function in terms of one variable based on te given information (sec 9) Be able to build a function from words (sec 9) f ( + ) f ( ) Be able to find and simplify difference quotient (sec 0) Any andout given in class, any class discussions Partial Review Eercises 5 Write te function in te form f ( ) a( ) + k : a) f( ) + ; b) y + + ;

2 c) f ( ) SLO (Student Learning Outcome) 0 Given f ( ) and g( ) 5 Find a) ( f g)( ) ; b) ( g f )( ) and give te domain for eac composition SLO 7 Solve te given equation: a) ; b) SLO If a projectile is sot vertically upward from te ground wit an initial velocity of 00 feet per second, neglecting air resistance, its eigt s (in feet) above te ground t seconds after projection can be modeled by s 6t + 00t SLO a) How long will it take for te projectile to return to te ground? b) Wen will it reac maimum eigt? c) Wat is te maimum eigt? 5 Sketc te grap SLO 5, 0 a) f ( ) ; b), < f ( ) ; c), < +, > +, < e) f ( ), <, y + 6 ; d) +, < 0 f ( ) ;, 0 6 An open rectangular bo wit a volume of ft as a square base Epress te surface area A of te bo as a function of te lengt of te side of te base SLO, 7 Find te number of units tat produce te maimum revenue, R 900 0, were R is te total revenue in dollars and is te number of units sold SLO 8 Given f ( ) 7, g( ), ( ) + 6 Find f g SLO 7 9 Given f() + ; g() SLO 7 Find a) f g; b) g f and give te domain for eac composition 0 Evaluate (if possible) te function f ( ) Simplify your answer SLO a) f(t); b) f(s+); c) f(/); d) /f(); e)f + ; f) f(+) f() Given f() and g() SLO 6 f Find a) ( g ) (); b) (fg)() and give te domain for eac combination f ( + ) f ( ) Find for te following functions: a) f() 7 ; b) c) f ( ) ; d) f ( ) + SLO 5 Use te graps to determine te domain and range of te given function SLO, 5 a) b) f ( ) + ;

3 Determine te domain for te given function SLO a) f ( ) b) f ( ) c) + 5 d) ( + ) f ( ) e) g( ) ( ) f) f ( ) + g ( ) 5 A farmer wants to enclose a rectangular field by a fence and divide it into two smaller rectangular fields by constructing anoter fence parallel to one side of te field He as 000 yards of fencing Find te dimensions of te field so tat te total area is a maimum SLO,, 6 Epress te area A of a circle as a function of its circumference C SLO, 7 Te graps of f and g is given SLO, a) State te values of f ( ) and g ( ) b) Estimate te solutions of te equation f ( ) c) On wat interval is f decreasing? d) State te domain and range of f e) State te domain and range of g 8 An open bo is to be made from a square piece of material centimeters on a side by cutting equal squares ( centimeters) from te corners and turning up te sides Determine te volume of te bo as te function of SLO, 9 Find te inverse function SLO a) f ( ) ; b) f() 5; c) y + ; d) y ( ), ; e) f ( ) + 0 A closed rectangular bo wit a square base is and eigt to be constructed from 00 square inces of material Epress te volume of te bo as a function of te lengt of te side of te base SLO, Use te table below to find te following values SLO 6, 7 f() g() Find a) (f g)(); b) (g f)(); c) (f + g) () Find te maimum or te minimum value of f ( ) SLO

4 Find te largest interval on wic f ( ) ( + ) is increasing SLO Epress te distance d, from a point (, y) on te grap of + y to te point (5, 8) as a function of SLO, 5 Determine te equation of te quadratic function wose grap is sown below SLO Determine weter eac of te given functions is even, odd, or neiter even nor odd SLO 6 6 a) f ( ) b) f ( ) 7 Find te equation of te line passing troug (-, ) and perpendicular to te line + y 9 SLO 8 8 Fund functions f and g suc tat F( ) f g SLO 8 a) F ( ) ( + ) ; b) F ( ) As dry air moves upward, it epands and cools If te ground temperature is 0 0 C and te temperature at a eigt of km is 0 0 C, epress te temperature T in terms of te eigt SLO 9 0 From ABC Wireless te montly cost for a cell pone wit 00 minutes per mont is $5, or 00 minutes per mont is $50 SLO 9 a) Given tat te cost in dollars is a linear function of te time in minutes, find a formula for te cost function b) Wat is te cost of 00 minutes per mont? Sketc te grap of a) / f( ) ( ) + ; b) / f( ) ( ) ; c) f ( ) + + SLO, 5 Find an equation of te line passing troug te points (,) and (-,5) SLO 7 Given f ( ) Find f ( ) and state te domain and range of f ( ) SLO 0 If f ( ) +, find te following SLO a) f ( a + ) ; b) ( f a ) ; c) [ f ( a)] ; d) f ( a + ) 5 Evaluate f ( + ) f () for te function f ( ) + SLO

5 f ( a + ) f ( a) 6 Evaluate for te function f ( ) SLO 7 A rectangle is inscribed in te parabola y + 5as sown, wit its base on te -ais SLO, Write te area A of te rectangle as a function of Answers: a) ( ) 7 ; b) ( ) + ; c) ( ) + 9 a) 6 5, D (,5] ; b) 5, D [ 0, ) a) ± 7 ; b) / ; 9 / 5 a) 65 s, b) 5/8 s; c) 65/ ft 5 a) b) c) d) e)

6 6 A + 8, > units 8 ( + 6) 7 9 a) ; D: + (,] ; b) + t 0 (a) ;(b) t s s ; D: (, ) [/, ) ; + ;(c), 0 ;(d), ;(e) + ; (f) + ( + )( ) a) ; D:[0, ) b) (a) 7 ; (b) + +; (c) ; D: [0, ] ; (d) ( + 5)( 5) (a) domain: [-, + ), range: [, + );(b) (,) (, ), range (,0) (0, ) (a) (-,+ ); (b) all s ecept -5; (c) (-/, + ); (d) (,) (, ) ; (e) [0,]; f) (, ) (,) (, ) by 750 C 6 A π 7 a) f ( ) ; g( ) ; b), ; c) (0,); d) Domain:[-, ], Range: [-, ]; e) Domain: [-, ], Range [5, ] 8 V() ( ) ; a) f ( ) ; b) ; c) ( ) +, ; d) + ; e) 0 V 75 a) 0, b), c) 5/ (, ] d y ( ) 6 (a) odd (b) even 7 y / + 9/ 8 a) f ; g + ; b) f ; g 5 9 T f ( ) 0 a) y b) $80

7 a) b) c) y -/ + / ( ) + f ; domain of f ( ) : (, ) (, ) ; range of f ( ) : (,) (, ) + a) a + a + ; b) a a + ; c) a a + 9a a + ; d) a + a + a a a 7 A( ) 0