Section+1.1

1.1- Modeling and Equation Solving

1. Numerical Modeling -situations where data is analyzed (using a table or a software like excel)

2. Algebraic Modeling - using formulas to relate variable quantities Example 3 (p. 71)

3. Graphical Model - visible representation of a numerical or algebraic model (quadratic, linear exponential?)

CAUTION: Grapher Failures (p. 78-79)

Example: Find y intercepts for y = 3/ (2x-5) There are none!!! Some calculators do show y intercepts, so be sure to always double check if the image on the calculator is correct by looking at a table, etc.

Homework- p. 81 1- 10, and p. 83 39 – 47 ODD

1. Plot the points on your calculator by pressing the STAT button then selecting choice 1 (Edit ) then hit GRAPH (if the points cannot be seen in your normal window hit ZOOM choice 9 [STAT])

2. Then observe the data and determine what type of graph is it

3. For the regression, go to STAT move your cursor to CALC and select the type of regression (4: linear regression, 5: quadratic regression, 6: cubic regression, etc)

1. d. (-3, 18) by (-3, 32), q. (y = 2x) x || 3 || 5 || 7 || 9 || 12 || 15 || y || 6 || 10 || 14 || 18 || 24 || 30 ||

2. f. (-1, 7) by (-4, 40), r. (y = x^2 + 2) x || 0 || 1 || 2 || 3 || 4 || 5 || y || 2 || 3 || 6 || 11 || 18 || 27 ||

3. a. (-2, 14) by (-4, 36), p. (y = 3x – 2) x || 2 || 4 || 6 || 8 || 10 || 12 || y || 2 || 3 || 6 || 11 || 18 || 27 ||

4. h. (-5, 30) by (-5, 100), o. (y = 10 – 2x) x || 5 || 10 || 15 || 20 || 25 || 30 || y || 90 || 80 || 70 || 60 || 50 || 40 ||

5. e. (-1, 7) by (-4, 40), l. (y = 40 – x^2) x || 4 || 8 || 123 || 14 || 18 || 24 || y || 5 || 7 || 9 || 11 || 13 || 15 || 6. b. (-1, 6) by (-2, 20), s. (y = 2x+3) x || 1 || 2 || 3 || 4 || 5 || 6 || y || 5 || 7 || 9 || 11 || 13 || 15 || 7. g. (-1, 16) by (-1, 9), t. (y= (x – 3) / 2) x || 5 || 7 || 9 || 11 || 13 || 15 || y || 1 || 2 || 3 || 4 || 5 || 6 ||

8. j. (-5, 40) by (-10, 650), k. (y = x^2 +x) x || 4 || 8 || 12 || 14 || 18 || 24 || y || 20 || 72 || 156 || 210 || 342 || 600 ||

9. i. (-3, 9) by (-2, 60), m (y = (x + 1) (x – 1)) x || 3 || 4 || 5 || 6 || 7 || 8 || y || 8 || 15 || 24 || 35 || 48 || 63 ||

10. c. (-4, 40) by (-1, 7), n. (y = √x –3 ) x || 4 || 7 || 12 || 19 || 28 || 39 || y || 1 || 2 || 3 || 4 || 5 || 6 ||

ALL ANSWERS IN THE BOOK FOR 39 – 45 ARE WRONG!

Can be done 1 of 2 ways-

1. Set the equation to 0 and then, graph the equation by selecting the Y= button (to type the equation) on your calculator and hitting the GRAPH button. Then find the x intercept by hitting 2nd TRACE, 2 (ZERO) find the zero on the x –axis.

2. Graph both equations separately by selecting the Y = button (to type the equation) and then hit GRAPH. Find the intercept of the lines by hitting 2nd TRACE, 5 (INTERSECT).

39. 2x – 5 = √ x + 4 41. │2x – 5│= 4 –│x – 3│ x = 3. 91  x = 4

43. 2x – 3 = x^ 3 – 5 45. (x + 1) ^ -1 = x^ -1 + x x= 1.77  x = -1.47

47. Swan Auto rental charges $32 per day plus $0.18 per mile for an automobile rental.

a. Elaine rented a car for one day and she drove 83 miles. How much did she pay? y = .18x +32 y = $46.94

b. Ramon paid $ 69.80 to rent a car for one day. How far did he drive? 69.80 = .18x + 32 __37.8__ = __.18x__ .18 .18 210 = x