f 2a.) f 4a.) increasing:

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1 MSA Pre-Calculus Midterm Eam Review December 06. Evaluate the function at each specified value of the independent variable and simplify. f ( ) f ( ) c. ( b ) f ) ). Evaluate the function at each specified value of the independent variable and simplify. f ) ( c.) f ( ) f () c. f (0) d. (). Find the domain of the given function. Use interval notation! ( ) f g ( ) c. 6 f ) ) c.) d.) ) ) c.). Use a graphing utility to graph the function and determine the open intervals on which the function is increasing, decreasing, or constant (use interval notation!). Identify any relative minimum or relative maimum values of the function. ( ) 9 f ) increasing: decreasing: constant: rel. min.: rel. ma.: ) increasing: decreasing: constant: rel. min.: rel. ma.:. Determine algebraically if the function is even, odd, or neither. Verify using a graphing utility. ( ) 6 f 6 c. ) ) c.)

2 6. Given, g ) ( ) ( ) 6 ( and h ) (. Describe the sequence of transformations from, g( ), or h() to j (). j j ( ) c. j ( ) 7 ) ) c.) 7. Given, g( ) and h ( ). Find the indicated values. ( f g)() ( f h)() c. ( fh )() 7) 7) g h d. e. ( f )( ) 7c.) g f. ( f h)( ) 7d.) 7e.) 7f.). Find the inverse of the function algebraically. 7 c. 0 ) ) 9. Show that f () and () g are inverses. c.), g ( ), 0 0. Epress each comple number in standard form a bi. i c. 7i 0) 0) 0c.) d. i i e. i f. i i i 0d.) 0e.) 0f.)

3 . Solve the following equations for. 7 c If P ( ), use synthetic substitution to find: P () P c. (i) ) ) c.) P ) ) c.). Solve for. 0.). Sketch the graph of the rational function by hand. Identify any -intercepts, the y-intercept, horizontal asymptotes, vertical asymptotes, and slant asymptotes. ( ) f -intercept(s) = y-intercept = H.A. = V.A. = S.A. = ) f -intercept(s) = ( y-intercept = H.A. = V.A. = S.A. =

4 c. -intercept(s) = y-intercept = H.A. = V.A. = S.A. =. Evaluate the following eponential epressions: 0 0 c. 9 d. ) ) c.) d.) 6. Solve each eponential equation: 7 6) 6) 7. Suppose $,00 is invested at an interest rate of 9.6%. How much is the investment worth after years if interest is compounded: Monthly? Continuously? 7) 7). Solve for.) 9. Simplify: 9) 7 9) c. 6 9c.)

5 0. Solve for : e e 0) 6 0) c. e e 0 0c.) 9 7 d. 0d.). Assume the value of a computer depreciates at a rate of % a year. Determine the value of a laptop computer five years after it has been purchased for $,70.. A researcher estimates that the initial population of honeybees in a colony is 00. They are increasing at a rate of % per week. What is the epected population in weeks?. In 990, Eponential City had a population of 700,000 people. The average yearly rate of growth is.9%. Find the projected population for 00.. Find the projected population of each location in 0: In Honolulu, Hawaii, the population was 6, in 990. The average yearly rate of growth is 0.7%. The population in Kings County, New York has demonstrated an average decrease of 0.% over several years. The populations in 997 was,0,.. The population of Los Angeles County was 9,,9 in 997. If the average growth rate is 0.%, predict the population in Radioactive gold 9 (9Au), used in imaging the structure of the liver, has a half-life of.67 days. If the initial amount is 0 milligrams of the isotope, how many milligrams (rounded to the nearest tenth) will be left over after: ½ day week 7. In 000, the chicken population on a farm was 0,000. The number of chickens increased at a rate of 9% per year. Predict the population in 00.. If Charlie invested $,000 in an account paying 0% compounded monthly, how much will be in the account at the end of 0 years?

6 9. Mike would like to have $0,000 cash for a new car years from now. How much should be placed in an account now if the account pays 9.7% compounded weekly? 0. Suppose $,00 is invested at 7% compounded quarterly. How much money will be in the account in: ¾ year year Answer Key Midterm Review Packet December 06 0 c. b c. d. 6,,, c.,, increasing:,, decreasing:, constant: none rel. min.:,, rel. ma.: increasing:, decreasing:, constant: none, 0 ; rel. ma.: none rel. min.:, 0 even neither c. odd 6 f () has a horizontal shift units left, reflects over the -ais and has a vertical shift 6 units down 6 f () has a vertical stretch of and a vertical shift up units 6c. f () has a horiz. shift units right, reflects over the -ais, a vertical shrink of ½ and a vertical shift 7 units down c. 7d. 7e. 7 7f. -97 ( ) f 7 c. 0, 0 9. Show that f g( ) g

7 i i c. 7 i 6 6 d. i 7 7 e. i f. 7 i c. 6 i., -intercept:, 0 ; y-intercept: 0, ; H.A.: y = ; V.A.: = ; S.A.: none -intercept: 0, 0 ; y-intercept: 0, 0 ; H.A.: y = ; V.A.: = and = -; S.A.: none c. -intercept: none; y-intercept: ; H.A.: none; V.A.: = ; S.A.: + 0, c. 79 d $.9 7 $ c. 0 -/ 0. 0c. 0, 0.69(ln ) 0d. -. Do not use formula. Do not use formula. Do not use formula. Do not use formula. Do not use formula. Do not use formula 6. Use formula 7. Use formula. Use formula 9. Use formula 0. Use formula

1. Evaluate the function at each specified value of the independent variable and simplify. f 2a.)

1. Evaluate the function at each specified value of the independent variable and simplify. f 2a.) Honors Pre-Calculus Midterm Eam Review Name: January 04 Chapter : Functions and Their Graphs. Evaluate the function at each specified value of the independent variable and simplify. f ( ) f () b. f ( )