Math 106 In Class Assignment 4 - Name é Section Group...

Unformatted text preview:Name é Section Group Members Review Activity Each problem is worth 1 point and credit will be all or nothing for each of the 10 problems. if a problem has more than one part, all parts must be correct for credit. You may work together on the problems, but you must write out your own solutions. Follow all directions carefully! 1. Determine the domain of the functions. State your answers in interval notationu. Box your answers. f E 0 '3; fl Z 3- fixi= .32 "X 35" 1 7 O 63?: 42% if) b = >< / ' g(x) J; 2 W 2: x g": h? /.,_....._...mwwmwvaMnm.mmgsmam,fiam.wan? x—l _. m V" c. h(x)=log2(x2_9) X l u it; 2. Given the functions f(x)= x/x+1 and g(x)= 2 x 2 , determine the following. Box your answers. *x {3; film? a (f+g)(0) : girl? 2: \i a C 537%" O a i as?) t: E lg d W4 b. The domain of ( f —g)(x). M WmWWWMWWM_M ED)? 1 2 Q l—xzi'D v . . x Z J: W 211,5 V3" W #— ~—-—« —-—~ M- -- m. 23%;? 3% c (g of )(x) : Mi (354R )1; M. MW J Q"é§ w. d. The domain of (g ofXx). be * b 2 "i - W. 'j'w "55$er EX" K v ya if D by; ' E/ El 9* E in")!& $2 ~i WW» but..." WWW WW ., W- m... m WE 3. Retail sales of prescription drugs have been increasing steadily in recent years. In 1995, retail sales hit $72 billion. By the year 2000, sales had grown to about $146 billion. a. Use the relation with t = 0 corresponding to 1995 to find a linear equation modeling the growth of retail sales'.""Box'your answer. Mag g}; \ (OW. it? 9 :j' 'Eflé'; W b. Discuss what the slope indicates in this context. i 2» Wattage- 31 1 LE g "W3 c. in what year will sales reach $250 billion? Box your answer. Mfg: (2% 1 it levee ; J "'Wmfi, Y '4' 4. Given the graph of f (x) below, answer the following. Give answers in interval notation where apprOpriate. a. Determine the domain off(x): {3'3}; a} b. Determine the range offlx): C7 X 00) ("12%. c. For what values ofx is f(x) > O ? . . . {P V.' ' l {a f .1: k? d. For what values ofXIs f(x) mcreasmg? \. 3M l ' '3 M5 aw" e. Determine the maximum value of f (x) if it exists. 33W; f. Determine the minimum value of f (x) if it exists. / f(—1)= _L__.__f(1) = __:.i___ g. Evaluate: f(—4)= 5. Find the inverse of each function, if it exists, and state the domain and range of the inverse functiOn. If it does not exist, state why. 9:. W». ..... , Inverse function: Efltfi r -i "m Domain of inverse: L5 . Domain of inverse: Range of inverse: Q 00 E 3] Range of inverse: 3;} ~v x, 2'1 o f: j .. x+h - x 6. Use the difference quotient formula, W to determine the difference quotient for the function f(x) = x2 + 3 . Simplify your answer completely. Box your answer. 7. Given the polynomial function g(x) = x4 —— 4x3 + 7x2 -— 6x + 2 , find the foilowing. a. Right-End Behavior: Asx —> oo, or g(x) ——) —oo . m%: i: 3&5 1? Vi {635% ~ 2x2 — 5x — 3 + 2 ' Let f (x) = Find the following, showing work or explaining as to how you found each 2 x + x —— 2 (even if you can do it in your head). Sketch and label the asymptotes and intercepts on the graph. Sketch a graph of f All Asym ptote(s): gwi : 0' 10. The number of bacteria in a culture is modeled by the function n(t) = 25e'" , where t is in hours. a. if there are 100 bacteria after 6 hours, determine the value of k. N w tale") warmer at; it '5 :8 M : lé ef is? b. Use the model to determine how many hours it will take for the number of bacteria to reach 400. Simplify your answer. ng L "if" it/ Number of hours: