The number of daily sleep hours can be used to determine the amount of available study hours.

Transcription

1 Neatly complete all parts and hand in Wednesday. Clearly label the functions, the endpoints, intercepts, asymptotes, etc. The number of daily sleep hours can be used to determine the amount of available study hours. 1) Generate the notation for this function. 2) Interpret f (15) 3) Interpret f 1 (15) 4) Algebraically generate the linear relationship formula given that 12 hours of sleep allows for 10.5 available study hours and 14 available study hours occurs with 8 hours of sleep. 5) Graph and label the function and state the calculator window used. 6) Determine the domain and range of the function. 7) Algebraically evaluate f (15). 8) Algebraically evaluate f( x) 7 9) Is the inverse a function? Why? 10) Complete the table where possible. x f(x) ) Show work to generate the average rate of change for all sets above for the completed table This problem has two parts. The first piece of this function uses an exponential formula on the interval 0 x 8 where the percent of clarity of the subject matter studied can be generated from the available study hours. 1) Generate the notation for this function. 2) Interpret (0,0.01) 3) Interpret f (11) 4) Interpret f 1 (0.63) 5) Algebraically generate the formula given (0, 0.01) and (8, 0.97). 6) Graph and label the function and state the calculator window used. 7) Determine the domain and range of the function. 8) Algebraically evaluate f (3). 9) Algebraically evaluate f( x) ) Is the inverse a function? Why? 11) Complete the table where possible. X 4 6 f(x) ) Show work to generate the average rate of change for all sets from the completed table

2 This is the continuation of the previous part. The second piece of the function uses a logistics formula on the interval 8 x 21. 1) Interpret (16, 0.53) 2) Use the calculator Logistic regression to generate a formula using values (8, 0.97), (16, 0.53) and (21, ). 3) Graph and label the function and state the calculator window used. 4) Determine the domain and range of this part of the function. 5) Algebraically evaluate f (12). 6) Algebraically evaluate f( x) ) Is the inverse a function? Why? 8) Complete the table where possible. x f(x) 9) Show work to generate the average rate of change for all sets from the completed table 10) Draw and label the sketch for part one and two joined together as one piecewise function. 11) Write the piecewise function definition for the sketch. A periodic function can be used to model the knowledge retention rate as a function of percent of clarity of the subject matter studied on the interval 0 x 1. (1, 0.96) Maximum 1) Generate the notation for this function. 2) Interpret f (0.77) Initial (0, ) 3) Interpret f 1 (0.28) 4) Generate a periodic formula given the sketch. 5) Graph and label one cycle of the function and state the calculator window used. 6) Determine the domain and range of the function. 7) Algebraically evaluate f (0.34). 8) Algebraically evaluate f( x) 0.69 Show work! 9) Is the inverse a function? Why? 10) Complete the table where possible. X f(x) 11) Show work to generate the average rate of change for all sets from the completed table

3 Write a formula for I (y), your income from an initial investment of $28,000 growing at an annual rate of 4.78%. Graph I (y). Indicate the domain and range of I (y). Write a formula for E(y), your yearly expenses of $45,000 growing by $2500 each year. Graph E(y). Indicate the domain and range of E(y). Let P(y) = I (y)-e(y) Graph P(y) and indicate the calculator window used. Graphically determine P(y)= 0 Interpret P(y)= 0 Let R(y) = I (y) E(y) Graph R(y) Evaluate R(30) Interpret R(30) Evaluate R(40) Interpret R(40) A final semester letter grade is determined by the percent of information retained by studying. Graph the function. F less than 63% D 63% to less than 72% C 72% to less than 83% B 83% to 94% A Over 94% 1) Graph and label the function. 2) Determine the domain and range. 3) Is the inverse a function? Why? If you sleep 6.5 hours what will be your letter grade?

4 Extra credit Part One: Use the table below. 1. Using the calculator linear regression to at least 5 decimal places, generate a Blood Alcohol percentage -level (BAL) formula for a 120 lb woman as determined by the number drinks of alcohol. Press 2 nd STAT etc. 2. Identify the independent and dependent variables for this problem. 3. Identify the domain and range. 4. Write the notation for this problem similar to y=f(x). 5. Graph and label the function and all unique points (intercepts, asymptotes, etc.) 6. State an appropriate calculator window for the sketch. Male Female Drinks Approximate blood alcohol percentage (by vol.) One drink has 0.5 US fl oz (15 ml) alcohol by volume Body weight 40 kg 45 kg 55 kg 64 kg 73 kg 82 kg 91 kg 100 kg 109 kg 90 lb 100 lb 120 lb 140 lb 160 lb 180 lb 200 lb 220 lb 240 lb

5 Part Two: Use the chart below. 1. Using the calculator exponential regression to at least 5 decimal places, generate a Relative risk formula as determined by the BAL (i.e. blood alcohol concentration). 2. Identify the independent and dependent variables for this problem. 3. Identify the domain and range. 4. Write the notation for this problem similar to y=g(x). 5. Graph and label the function and all unique points. 6. State an appropriate calculator window for the sketch. % Standard drink chart (US) Amount (fl oz) Serving size Alcohol (% by vol.) 1.5 One shot 40 5 One glass One can 5 Alcohol 0.6 US fl oz (18 ml) 0.6 US fl oz (18 ml) 0.6 US fl oz (18 ml)

6 Part Three 1. Using Parts One and Two above, write a formula for g(f(x)). 2. Interpret g( f (6)). 3. Evaluate g( f (6)).