Technology Prerequisites. Date HW # 1: Get Course Expectations signed HW # 2: WS Review For Precalculus - #1-9 HW # 3:

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1 MATH 4R Technology Prerequisites NAME Date HW # 1: Get Course Expectations signed HW # 2: WS Review For Precalculus - #1-9 HW # 3: WS Review For Precalculus - #10-19 HW # 4: WS Review For Precalculus - #20-26 HW # 5: WS Study for electronic quiz (Use mix review # for practice) - #

2 MATH 4R REVIEW FOR PRECALCULUS NAME DATE Linear Functions Finding slope and the equation of a line using the Geometry menu. Finding x and y intercepts using Point On. Graphing lines using the Graph/Entry/Edit menu. 1. Find the slope of the line. 2. Using technology only, find the slope and the equation of the line that passes through the points (3, -8) and (9, 8) 3. Find the x-intercept and y-intercept then sketch for the line -3x + 5y =

3 4. Graph the line: 2x 3y Graph the line: 3x 5y Write the equation of the line passing through the points (-2, -4) and (4, 2) by plotting points and draw the line in the Geometry menu. 3

4 Functions Evaluating functions using a Graph page. Evaluating functions using the calculator page in conjunction with the Define function and the Such That command. 7. Given the function f1(x) = 1, find each of the following (x+5)(x 6) f1(4) f1(0) f1(6) 8. Using the such that symbol, find f -7 ( ) when f x) x (. 9. Define the function g(x) = x 2 + 2x 6 and find the value of g( 3) 10. Evaluate each of the following functions at x = 0, x = 3 and x = 7. f(x) = x 2 6x + 12 g(x) = x 3 + 2x 2 29x + 42 h(x) = x 3 x 2 2x + 2 p(x) = 2x 2 9x 5 r(x) = 5x

5 Quadratcis and Others Using the Analyze menu and the Geometry menu in conjunction with a Graph Page to find x and y intercepts, polynomial zeros, maximum and minimum points. Using the polyynomial root finder menu for rational, irrational and imaginary roots. 11. Graph using the window below and find the intersection point(s) for the two functions below: 2 V ( x) 2x 30x 144 W(x) = 27x Graph y = -x 2 + 2x The daily measurements (in particles) of a certain type of pollen during the 2 month of June is approximated by the function P( x) 26 48x 2x, where x is the day of the month with x 1 representing June 1. What is the maximum pollen count and when does this occur? (Graph P(x) using the window below) 5

6 14. If a rock is thrown upward from the edge of a cliff, its height H (in meters) after x seconds is approximated by H(x) = -4.9x x +10. a) Sketch the graph on the TI-Nspire using the window below b) What is the maximum height of the rock? c) When does the rock strike the ground? 15. On a calculator page, using Algebra s Polynomial Tools, find the root of the following polynomials: x 2 6x + 12 = 0 x 3 + 2x 2 29x + 42 = 0 x 3 x 2 2x + 2 = Using a Graph page, find the polynomial zeros (roots) of the folloing functions: f1(x) = 2x 2 9x 5 f2(x) = 5x f3(x) = x 3 x 2 2x + 5 6

7 Function Rules and Transformations Using the graphing page to identify a transformation. Using the Calculator page in conjunction with a Graph page to evaluate a tranformation function. 17. Find f1 f2(3) if f1(x) = 7x + 13 and f2(x) = 2x Match the correct function to the given graph. (A) f (x) = x - 2 (B) f (x) = x - 2 (C) f (x) = x + 2 (D) f (x) = x Using a calculator page Define functions f(x) = x 4 and g(x) = 10x + 4 anf find f(g(8) Using a Graph page or a calculator page, f1(x) = x 4 and f2(x) = 10x + 4 find f2(f1(8)). 10 7

8 21. Using the Geometry menu(point on, segments and measurement) on a Graph page, constuct the function below and find the slope of each segment Regression Usind a List and Spreadsheet page enter data appropriately. Using the List & Spreadsheet or a Calculator page find the curve of best fit. 22. The following data represents the amount of money Tom is saving each month since he graduated from college. Determine the line of best fit. Month Savings $52 $70 $81 $91 $102 $118 $ Michael depostited $200 into a bank account and did not make any further deposits or withdrawals. The accompanying table shows the account balance for several years. Which type of regression equation would best model this data? Linear, Exponential or Power? 8

9 Trigonometry 24. Sketch the graph using Zoom Trig then change window settings to (a) y = 3 sin(2x) (b) y = 2 cos( 1 2 x) 25. Find the approximate value of the expression rounded to two decimal places. (a) cos 49 (b) 3 tan Solve the equation for solutions in the interval 0 θ 360 using a Graph page. Using the calculator page, convert your solution(s) to degrees. 2cos 1 0 9

10 Mix Review 27. Graph the line: 5y 4x Find the point(s) of intersection: for 2x 3y = 6 and x 2 3x = y 29. Plot the points, draw the line through the points, determine the equation of the line for (-8,0) and (-4,5) 30. If friction is ignored, the time t (in seconds) required for a block to slide down 2a an inclined plane is given by the formula t where a is the g sin cos length (in feet) of the base and g 32 feet per second is the acceleration of gravity. How long does it take the block to slide down an inclined plane with base a 15 when 60? Round the final answer to the nearest tenth of a second. 10

11 31. Identify the graph that matches the equation f ( x) x The world population (in billions) for the years 1983 through 1994 is given in the table, where x 3 corresponds to {Source: U.S. Bureau of the Census, International Database.} y x y (a) Use the regression capabilities of a graphing calculator to fit a linear model to the data. Sketch the scatter plot and the regression line and write the equation of the line. (Round to the nearest hundredth. (b) Use the regression capabilities of a graphing calculator to fit an exponential model to the data. Sketch the scatter plot and the regression model and write the regression equation. (Round to the nearest hundredth.) 33. On a calculator page, using Algebra s Polynomial Tools, find the root of the following polynomials: 2x 2 7x 15 = 0 x = 0 11