Review for Final Exam Show your work. Answer in exact form (no rounded decimals) unless otherwise instructed.

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Review for Final Eam Show your work. Answer in eact form (no rounded decimals) unless otherwise instructed. 1. Consider the function below. 8 if f ( ) 8 if 6 a.

1 Review for Final Eam Show your work. Answer in eact form (no rounded decimals) unless otherwise instructed. 1. Consider the function below. 8 if f ( ) 8 if 6 a. Sketch a graph of f on the grid provided. b. What is the domain of f? [-, 6) c. What is the range of f? [-8, 8] d. Evaluate f ().- e. State where f is increasing. (0,) f. Find all values where f ( ). X=, =-. Use the graph of polynomial function f to estimate the following. Use interval notation where appropriate. Where is f increasing? (-.3,0) U (.8, ) Local Min: -10.9, -3. Local Ma: 0 Absolute Min: Absolute Ma: none Minimum possible degree of f : Is leading coefficient negative, positive or cannot be determined? positive y 8 y=f() 6 (0,0) (.8,-3.) (-.3,-10.9) Algebraically solve the following equations for real or comple solutions. Be sure to simplify all answers and check for etraneous solutions when appropriate. a. 5 b. 6 c. 65 =-±i =5 =5, -5, -5i, 5i d e f. 3 1 = or -1 = =-3/. Write the factored form of the fifth degree polynomial that has a vertical intercept of (0, 3). The zeros of the polynomial include, 1, 1, and i. f()=-(-)(+1)(-1)(+i)(-i) or f()=-(-)(+1)(-1)( +)

zeros. f()=-7(+1)( 3 )(-) 6. For each of the following, find the polynomial function with the given graph. Leave your an

Degree 5, leading coefficient is either 1 or 1 f()=1/(+)(-1)(-) f()= (-) 3 7.

Note: Include multiplicity, so a zero with multiplicity 3 counts as 3 zeros. a. Degree b.

2 Page of 7 5. Write the factored form of a polynomial with leading coefficient 7 which has the zeros 1 (multiplicity 1), 0 (multiplicity 3), (multiplicity ), and no other zeros. f()=-7(+1)( 3 )(-) 6. For each of the following, find the polynomial function with the given graph. Leave your answer in factored form. a. Degree 3 (you ll have to find the leading coefficient) b. Degree 5, leading coefficient is either 1 or 1 f()=1/(+)(-1)(-) f()= (-) 3 7. For each of the following, give the total number of zeros, the number of real zeros, and the number of nonreal zeros. Note: Include multiplicity, so a zero with multiplicity 3 counts as 3 zeros. a. Degree b. Degree 5 Total number of zeros: Number of real zeros: Number of nonreal zeros: Total number of zeros: 5 Number of real zeros: 5 Number of nonreal zeros: 0 5( )( ) 8. Consider the rational function g( ). ( )( 5) a. Find the coordinates of any holes in the graph. (-, 5/3) b. Give the equation(s) of any vertical asymptote(s). =5 c. Give the equation(s) of any horizontal asymptote(s). y=5/ d. Give the coordinates of the vertical intercept. (0,1) e. Give the coordinates of any horizontal intercepts. (,0) f. Graph the function on the given aes. Properly locate all the features in the preceding questions.

5 9. The concentration of a drug in a medical patient s blood stream is given by the formula d() t t 1 where the input t 0 is in hours and the output is in milligrams per liter. a. Label the aes of the graph.

3 5 9. The concentration of a drug in a medical patient s blood stream is given by the formula d() t t 1 where the input t 0 is in hours and the output is in milligrams per liter. a. Label the aes of the graph. mg/l b. Use the formula to determine the concentration of the drug at 1 hour. Interpret your result with a complete sentence..5 mg/l c. Determine the average rate of change of the drug from 1 hour to 3 hours. Represent your result graphically. Interpret your result with a complete sentence. -1 mg/l per hour Page 3 of 7 time 10. The number of meters a car travels in seconds is given by the function f 5 7. The graph for this function is shown to the right. a. Categorize this function as constant, linear, or nonlinear. b. Use the function f to evaluate the difference quotient f h f h. m=30 =10+5h c. Evaluate the difference quotient you just found using the values 1 and h. Write a complete sentence interpreting your result in contet. 30 m/s d. Represent your result on the given graph. That is, draw and label the line segment that corresponds to the number you got as the answer to the previous question. (see graph) 11. A tank contains 60 gallons of water at noon. Starting at 1 pm, water is drained from the tank at a rate of 30 gallons per hour for hours. Let g be a function representing the volume of water in the tank from noon to 3 pm, where is the number of hours past noon. a. Graph g on the given aes. b. Find a formula for g. g < 3

4 1. Consider the function with formula Page of 7 f For each of the following, write the formula for the function g whose graph is similar to f but satisfies the given conditions. Do not simplify the formula. a. Function g is found by shrinking f vertically by a factor of 1. g()=1/(8-10-6) b. Function g is found by shifting f right units and up 6 units. g()=8(-) -10(-)-6+6 c. Function g is found by reflecting f across the -ais. g()=-(8-10-6) d. Function g is found by reflecting f across the y-ais. g()=8(-) -10(-) The point (16, 1) lies on the graph of y f. Determine a point that lies on the graph of a. y f b. y f c. y f d. y f (16, 8) (0,1) (16, -8) (, 1) 1. Find the inverse of the following functions. 3 8 a. f 1 g c. h b. 1 for 0 f -1 ()= +8 3 g -1 ()= 1 h -1 ()= 15. Answer the following about functions f and g represented by the graphs below. Graph of f : Graph of g: a. f g 0 b. f g 1-1 c. f 1 d. g 1 e. f g f. g f g. f g 0 h. g 0 Not defined - Not defined

Page 5 of 7 16. In the year 000, the population of Clackamas County was 338 thousand people. In 006, the population was 37 thousand. a.

5 Page 5 of In the year 000, the population of Clackamas County was 338 thousand people. In 006, the population was 37 thousand. a. Letting 0 represent the year 000, find a function of the form f ab to model the population of Clackamas County. Work algebraically, and round to three decimal places. f()=338(1.017) b. According to the eponential model you found in part (a), what will the population be in 00? 73.5 thousand (73, 500) c. When does your model predict the population of Clackamas County will reach 00,000? Work algebraically, and round to the nearest year (whole number) Algebraically find the model f ab so that it satisfies the given conditions (round to 3 decimal places). a. f 0 and f 7.7 b. f 3 and f f()=(1.0) f()=3.577(1.035) 18. Consider the function f 3. a. What is the domain of f? (-, ) b. What is the range of f? (0, ) c. Give the equation of the asymptote. y=0, y coordinates of the vertical intercept. (0, 3) d. Give the e. Graph the function on the given aes. Accurately plot at least three points on your graph, and make sure your graph is consistent with your answers to the preceding parts of this question. f. Find the inverse function of f. f -1 ()=log Alice deposits $000 in a savings account earning.6% interest per year. Alice will leave the money in the account for 15 years. Algebraically answer the following questions and show work. a. Find the balance, to the nearest cent, if the money is compounded monthly. $ b. Find the balance, to the nearest cent, if the money is compounded continuously. $ c. If the money is compounded continuously, algebraically determine how long will it take for the initial deposit to triple. Round your answer to the nearest tenth..3 years to triple

6 0. Consider a 50 gram sample of iodine-131 whose half-life is 8 days. a. Find a function that gives the number of grams of iodine-131 remaining after days. Page 6 of 7 f()=50(.917) b. Algebraically determine how much of the 50 gram sample of iodine remains after 0 days. 8.8 grams c. Algebraically determine how many days would it take for the 50 gram sample to decay to grams. 37 days 1. Evaluate the following. Give eact values when possible; otherwise, round to four decimal places. a. log5 5 b. log6 6 1/ c. 1 lne 1. Use the logarithm rules to epand the following completely. a. 3 ln ab = 3 ln a+ ln b-8 ln c b. 8 c log d. log = ½ log( +1)-⅓ log ( +) 3. Use the logarithm rules to rewrite each of the following as a logarithm of a single epression. a. 3log 5log y =log 3 ln ln 1 =ln ((+)(-1) ) 3 y 5 b.. Solve the following equations. Give eact values when possible; otherwise round to four decimal places. a. 8 1 b c. log log 5 1 -/ d. ln 5 1 e. log3 5 0 f /5 log 7 log 1 log6 5. A herd of Tule Elk was introduced into the Point Reyes National Seashore in The number of elk found there over the net 10 years are shown below. Years since Number of elk a. What kind of function should you use for f : linear, eponential, or logarithmic? b. Use your calculator to find the appropriate regression formula for the function f. Write your answer below, rounding to three places after the decimal. f 13.07(1.8) c. Use your function to evaluatef 11, rounding to the nearest whole number. Interpret your answer using a complete sentence. 1003

6. Consider the function log 1 f. a. State the domain of f. b. State the range of f. c. Give the equation of the asymptote., y coordinates of the horizontal intercept. d. Give the e. Graph the function on the given aes.

7 6. Consider the function log 1 f. a. State the domain of f. b. State the range of f. c. Give the equation of the asymptote., y coordinates of the horizontal intercept. d. Give the e. Graph the function on the given aes. f. Find the inverse of f. Page 7 of 7 7. Find the sum of the following. Show all work. 5 a. k 5 b. n 5n k 3 c n0 0 k 15 10n 8. Epand 6 and simplify Epand 3 and simplify Epand 3y 5 and simplify y+70 3 y y y +3y A soda can at 76ºF is put into a cooler containing ice at 3ºF. The temperature of the soda can after t minutes is modeled by the formula T t 3 (0.97) t. Algebraically determine how long will it take 19.9 for the soda can to cool to 56ºF? Round answer to the nearest tenth of a minute. Interpret your result with a complete sentence.

Two-Year Algebra 2 A Semester Exam Review

Two-Year Algebra 2 A Semester Exam Review Semester Eam Review Two-Year Algebra A Semester Eam Review 05 06 MCPS Page Semester Eam Review Eam Formulas General Eponential Equation: y ab Eponential Growth: A t A r 0 t Eponential Decay: A t A r Continuous