ACTIVITY.. Use the regression capabilities of our graphing calculator to create a model to represent the data in the table. - - 0. -. ACTIVITY. Determine the -intercept and end behavior of each function. 7. = 7 - + 8 + 6 8. = - + 9 - + 0 + 9 Use what ou know about end behavior and zeros to graph. 9. f () = ( - )( - 6)( + )( + 7). Graph the function ou found in Question and list the important features of the graph.. List the important features of the graph below. Approimate non-integral values. 6 0. f () = ( - ) ( + )( - ) 6 6 6 00 College Board. All rights reserved.. Without using a calculator, find the end behavior and - and -intercepts of f () = ( + )( - )( + )( - 9)( + ).. Without using a calculator, find the end behavior, maimum possible zeros, and maimum possible turning points of f () = 9 + 6 - + -. 6. Use a graphing calculator to find the zeros, turning points, -intercepts and end behavior of f () = - - 0 + 0 + 6. Determine all the rational zeros of f () = - + - + 6.. Sketch a possible graph of f () = - - - 6 -. Determine the possible number of positive and negative real zeros of h() = + + - +.. Graph f () = - - 6 + 6. Unit Functions and Their Graphs
ACTIVITY. Find a polnomial with real coefficients of lowest degree with the given zeros.. Degree, zeros = -,, 6. Degree, zeros = -, -, -, 0, Find the zeros of the following polnomials and write them as a product of comple factors. 7. f () = + 8. f () = - Rewrite the polnomial functions as a product of comple factors. 9. f () = - 6 0. f () = + 8 - - 6 Find the zeros of each function.. f () = - 9 -. f () = - 77 +. Find all the zeros of f () = + - +, given + i is a zero. Solve each inequalit and write the solution interval.. - 6 9. - + > 0 ACTIVITY. 6. Anita is four times as old as her daughter Nia. Nine ears from now, Anita will be two and a half times as old as Nia. a. What is Anita s age? b. Let R() represent the ratio of Anita s age in ears to Nia s age in ears and let represent the number of ears from now, either past or future. Write R as a function of. c. If ou were to graph the ratio of their ages in ears, where = 0 represents the present, at what value of would the graph appear to become vertical? What does this mean in terms of their ages? Use a graphing calculator and R() = + -. 7. Determine where the function is unbounded. 8. Find the equation of the vertical asmptote. 9. Find the equation of the horizontal asmptote. 00 College Board. All rights reserved. SpringBoard Mathematics with Meaning TM Precalculus
00 College Board. All rights reserved. ACTIVITY. Sketch a graph of each function or pair of functions. 0. f () = and g () = -.. f () = +.. f () = -.. f () = - - +. Find the horizontal asmptote. a. f () = + 8 - - b. g() = - 9 + - 7. Find the horizontal asmptote. a. f () = 8 - + 7 b. g () = + + 6 + - + - 6. Find the - and -intercepts. a. f () = + + + b. g () = - 6 + 7. Sketch a graph of each function without using a graphing calculator. a. f () = - + + b. g () = + 7-8 8. Sketch a graph of the following. a. f () = - + - b. g () = - 8 + - 9. Find the equation of the slant asmptote. a. f () = + + b. g () = + + + ACTIVITY.6 Determine the balance in each account for an initial investment of $8,000. 0. ears at % interest, compounded annuall. ears at % interest, compounded annuall. 0 ears at.% interest, compounded quarterl. ears at % interest, compounded continuousl. 0 ears at.% interest, compounded continuousl The Tameri tree was introduced to a region in 006 and has been growing eponentiall.. The initial population was 0 trees and the population is increasing at an annual rate of %. Create a continuous eponential function that represents the number of Tameri in the region in a given ear since the first population was measured. 6. In what ear will the population of trees reach 00? 7. A new car was purchased in 00 for $0,000. It depreciates at a rate of 9%. Create a continuous eponential function that represents the value of the car after t ears of ownership. 8. When will the car have a value of $0,000? Unit Functions and Their Graphs
ACTIVITY.7 9. Evaluate lo g 6 ( ) 0. Which of the following can be used to find log 8? a. ln 8 b. log 8 ln log 8 c. ln d. ln 8 ln 8. Epand ln z.. Epand ln.. Write ln ( - ) - ln ( + ) + ln as a logarithm of a single quantit. Solve.. 00 e - =. 00 - + e = 7 6. log = 6 7. ln = Solve. Check our solutions. 8. log + log( + ) = ACTIVITY.8 Use the graph of f () for Questions 9 6. Sketch each graph below. 9. = f () 60. = f ( - ) 6. = -f () 6. = f () - Determine if the following functions are odd, even or neither. 6. f () = 6. f () = e - 6. f () = Find the sum, difference, product and quotient and composition of the functions in each question below. State the domain. 66. f () = - 7, g () = -8-9 67. f () =, g () = - 00 College Board. All rights reserved. SpringBoard Mathematics with Meaning TM Precalculus
00 College Board. All rights reserved. Use the graph from Activit.8 on the previous page. 68. Sketch the graph of = f () 69. Which of these is the graph of = f ( )? a. b. c. d. ACTIVITY.9 The swim coach decides to put chlorine in the swimming pool to control the algae concentration. These are the readings after the chlorine is introduced. Da Algae Concentration (ppm) 00 0 99 6 70. Make a scatter plot of the data. 7. What do ou notice about the scatter plot? 7. Perform a least squares regression for the data. a. Give the equation of the regression line and graph the regression line on the scatter plot. b. What is the correlation coefficient for the data? c. What does this coefficient indicate about the data? 7. What tpe of transformation can be used on the data to make the scatter plot appear more linear? 7. Transform the data and complete the table below. Da Algae Concentration (ppm) ln() 00 0 99 6 a. Calculate the linear regression for the transformed data. b. Find the correlation coefficient. c. compare the correlation coefficient to the previous result. What does this indicate about the transformed data? 7. When can the coach epect the algae concentration to be less than ppm? Eplain our answer. Unit Functions and Their Graphs