Review 3
Domain/Range/Function: Domain are the possible x values. Independent Variable
Range are the possible y values. Dependent Variable
Recursive: If it is arithmetic (adding/subtracting numbers) then NEXT=NOW + #
If it is geometric (mult/dividing) then NEXT = NOW * #.
(Do 2nd#/1st# )
Rate of change: (Last y – First y)/(Last x – First x)
Ex: y = 2x from [1,7] à (27 – 21)/(7 – 1)
Shifting Y = ~~~~~~ + c will shift the graph up c
Y = (x-b)2 or 3x-b or f(x – b) will shift the graph RIGHT B
Ex: (x -2)2 + 3 is shifted right 2 and up 3
Exponential (y=abx) vs Quadratic (x2) vs Linear (ax + b)
Exponential will always produce a larger y when x is large….
Regressions:
A) Turn Diagnostic ON: 2nd 0 Scrolldown to Diagnostic On ENTER ENTER
B) Turn Statplot On: 2nd y= look for ways to turn statplot on
C) Identify the x’s (independent variable) and y’s (dependent variable).
If there are years, then make the first year ‘0’ and then subtract each year from the first year.
Ex: 1950, 1956, 1968 would become 0, 6, 18
D) Put the Data into the calculator.
STAT 1 Put the x’s into L1; Put the y’s into L2; ( You can reset your calculator by 2nd MEM 7 1 2
E) Plot your data: ZOOM 9 ENTER
F) Find your regression equation:
Linear: STAT à 4 ENTER
Exponential: STAT à 0 ENTER
G) Interpret the Data (and write it down with three non-zeros)
Linear: y= ax + b. The ‘a’ becomes the ‘m’ in y=mx + b and is SLOPE, CHANGE, etc…
Exponential: y =a(b)x and a is the initial value and b is multiplier
H) Type the prediction equation into Y=.
I) Look at the table to find the missing x or y. You can use ‘Tableset’ ( 2nd Window ) to
get x’s closer to the desired x-value or solve it by graphing
Coefficient of Correlation: ‘r’ the closer it is to 1 or -1 the stronger it is
Residuals: The actual values minus the predicted values
1. f(x) = x2 – 3x + 2. The domain of f(x) is {1,3,5,7}. Find the range.
2. Jack has only quarters and nickels in his pocket. He has a total of $1.50 in his pocket. Assume that quarters are the
domain. What are all possible members of the domain?
3. A hot tub contains 1200 gallons and is being drained. Every hour the volume decreases by 60 gallons.
a) Write an equation that models this situation.
b) Identify the independent and dependent variables.
c) Identify the practical domain and range.
4. Write the NEXT-NOW statements for the following
a) 8, -10, -28 b) 25, 20, 16 c) #3 from above d)
e) f) The value of a house increases 4.3% a year. In 2010, it was $200,000
X / 2 / 3 / 4Y / 4 / 10 / 16
5. Find the rate of change of the following:
a) (5,6) to (8,9) b) 4d from above c) Y = 3x + 9 from [1, 4]
d) Y = 2x from [3,5] e)#4e from above f) X2 + 4x + 2 from [1,5]
6. a) How is f(x – 3)+ 2 shifted from f(x)? b) How is 2x+1 shifted from 2x + 1?
c) How is (x + 3)2 + 1 shifted from (x – 2)2 + 1? d) Which equation represents 3x+1 + 2 shifted 3 left
and 4 down?
7. Lucy wants to invest $3000 into a financial plan. Two financial institutions offer the following choices:
A: y = 3000 + 150x B: y = 3000(1.015)x
a) Describe each plans in words
b) Which plan is better for Lucy after 1 year? After 10 years? After 30 years?
8.
a) f(x) and g(x) are graphed to the left: b) h(x) = 2 i(x) = x2 – 2. Graph h(x) + i(x) from
Graph f(x) + g(x) on interval [-1,3] [0,3]
9. Suppose that the average price of gasoline is given by the equation
Year / 2000 / 2001 / 2003 / 2005 / 2007Price of Gasoline $ / $1.30 / $1.47 / $1.48 / $1.82 / $2.27
(Data taken from http://data.bls.gov/cgi-bin/surveymost)
a) Write an equation that best fits this situation (let x=0 for 2000)
b) What is the average price increase per year?
c) Describe the correlation
d) What was the predicted cost of gasoline in 2008?
e) Find the residuals and determine which year had the highest redsidual
10. The table shows the Richter scale that measures earthquake intensity.
Richter Number / 4 / 5 / 6 / 7 / 8Increase in magnitude / 1000 / 10000 / 100000 / 1000000 / 10000000
a) What type of equation is the best model (linear, quadratic, or exponential)
b) Write the prediction equation. Specify what x and y are:
c) Predict the increase of magnitude for a 7.2 earthquake.
d) Predict the ricther scale number for an increase of 5000000 in magnitude
11. Find (or estimate) the coefficient of correlation
a) (0,2) (1,8) (3, 11) (4, 19) b) c)
12. f(x) = 3x + 2. The RANGE is {8,11,14}. Find the DOMAIN
13. Mr. Thompson is making a 30 pt. quiz that only contains True/False equations worth 3 points and Multiple Choice questions that are worth 5 pts. What are the possible members of the domain? <True/False are the x values>
14. f(x) = 2(1/2)x+2 g(x) = 2(1/2)x + 3. How is f(x) different from g(x)?
15. The function h(x) = 2(1/2)x is replaced with h(x) + k. What is k?
16. Fred and Gail’s grandmother decided to give them money monthly in a different manner. Both started with $20. Fred’s grandmother added $75 each month. Gail’s grandmother doubled it every month. At the end of which month will they receive the same amount of money?
17. What is the average rate of change in problem #9?
18. Alberto turned the faucet on in a bathtub and then measured the depth of the water at 1-minute intervals. His data is displayed in the table below:
Time (min) / 1 / 3 / 6 / 9 / 12 / 15Depth (cm) / 3 / 7 / 12 / 20 / 26 / 33
a) Find the linear equation of best fit.
b) Identify and interpret the slope.
c) Identify and interpret the y-intercept represent.
d) Predict the water depth after 16 minutes.
e) Predict when the water will be 38cm.
f) What percentage of the residuals was higher than 1cm?
19. A scientist recorded the growth g (in inches) of pine trees and the amount of rainfall r (in inches) they received in their first year.
R (in.) / 0 / 3 / 5 / 12 / 17 / 22 / 34 / 35 / 45G (in.) / 1 / 4 / 6 / 9.5 / 10.8 / 10.9 / 6 / 5.3 / 1
a) According to the correlation coefficients, which model best fits the data? (linear, exponential or quadratic)
b) Write the equation that best fits the data:
c) According to your equation, find the height of a pine tree with 28 inches of rainfall in its first year.
20. The table below shows the population of two towns.
Year / Population of Springtown / Population of Summertown2010 / 20,000 / 20,000
2011 / 21,900 / 25,000
2012 / 24,100 / 31,250
2013 / 26,000 / 39,063
a) Which town is growing linearly? How much is it increasing by?
b) Which town is growing exponentially? How much is it increasing by?
c) What is the rate of growth for each town from 2010-2013?
d) Write the NEXT-NOW equations for both towns.
e) Write an equation that demonstrates the growth of both towns.
f) Predict the population in 2015 for both towns.
21. The table below shows the total cost at a restaurant for different amounts of people:
Number of People / 1 / 2 / 3 / 4Total Cost of Bill / $15 / $22.50 / $30 / $37.50
Which function below represents the cost at a restaurant for ‘n’ amount of people?
A. C(n) = 15n B. C(n) = 15 + n C. C(n) = 7.50n + 1 D. C(n) = 7.50(n – 1) +15
22. The balance in an account at the end of year can be represented by the formula . The account was opened 6 years ago, the balance at the end of 3 years was $2,034.56. What was the balance at then of 6 years?
A. $31,400 B. $29,200 C. $25,300 D. $21,900
23. The amount of people in a waiting room can be represented by the formula NEXT = NOW + 2. At the beginning of the day, 6 people are waiting. How many people are waiting 5 hours later?
A. 10 people B. 12 people C. 14 people D. 16 people
24. The water filling up in a bathtub is modeled by the equation V=.4t + 3 where V is the volume (gallons) and t is the time (minutes) after 8:00 P.M. What is the meaning of the y-intercept in the problem?
A. The average rate that the bathtub is filling up B. The amount of water in the tub once it is filled
C. The amount of water at 8:00 PM D. The amount of gallons the bathtub is increasing by each minute.
25. What is the meaning of the slope in 24?
A. The average rate that the bathtub is filling up B. The amount of water in the tub once it is filled
C. The amount of water at 8:00 PM D. The amount of gallons the bathtub is increasing by each minute.
26-27.
26. Which of the following statements best describes the correlation:
A. There is a strong negative relationship.
B. There is a weak negative relationship.
C. There is a strong positive relationship.
D. There is a weak negative relationship.
27. Which point has the highest residual?
A. A B. B C. C D. D