1. Chapter 5 Functions and their Graphs

2. Function Notation f(t) = h Independent Variable Dependent Variable Example h = f(t) = 1454 –16t 2 When t= 1, h= f(1)= 1438, We read as “f of 1 equals 1438” When t = 2, h = f(2) =1390, We read as” f of 1 equals 1390 “

3. Ch 5.1 (pg 251) Definition and Notation Example – To rent a plane flying lessons cost $ 800 plus $30 per hour Suppose C = 30 t + 800 (t > 0) When t = 0, C = 30(0) + 800= 800 When t = 4, C = 30(4) + 800 = 920 When t = 10, C = 30(10) + 800 = 1100 The variable t in Equation is called the independent variable, and C is the dependent variable, because its values are determined by the value of t This type of relationship is called a function A function is a relationship between two variables for which a unique value of the dependent variable can be determined from a value of the independent variable tc 0800 4920 101100 (t, c) (0, 800) (4, 920) (10, 1100) Table Ordered Pair

4. Using Graphing Calculator Pg 258 Enter Y1= 5 – x 3 Press 2 nd and table Enter graph

5. Ex5.1, pg 264-265 No. 40 g(t) = 5t – 3 a)g(1) = 5(1) – 3 = 2 b)g(-4) = 5(-4) – 3 = -20 – 3= -23 c)g(14.1) = 5( 14.1) – 3= 70.5 – 3= 67.5 d)g = 5 – 3 = - 3 = No. 51. The velocity of a car that brakes suddenly can be determined from the length of its skid marks, d, by v(d) =, where d is in feet and v is in miles per hour. Complete the table of values. Solution. V(20) Similarly put all values of d and find v d205080100 v15.524.531.034.6

6. Ch 5.2 Graphs of Functions (Pg 266) Reading Function Values from a Graph 12 13 14 15 16 19 20 21 22 23 October 1987 Dow Jones Industrial Average Dependent Variable 2500 2400 2300 2200 2100 2000 1900 1800 P (15, 2412) Q (20, 1726) Time Independent Variable f(15) = 2412 f(20) = 1726

7. Vertical Line Test ( pg 269) A graph represents a function if and only if every vertical line intersects the graph in at most one point Function Not a function Go through all example 4 ( pg 270)

8. Some basic Graphs b = 3 a if b 3 = a Absolute Value -10 - 9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 Six Units So absolute value of a number x as follows x = x if x > 0 - x if x< 0

9. Graphs of Eight Basic Functions y = x 2 g(x) = x 3 f(x) = f(x) = f(x) = 1/ x g(x) = 1/ x 3 f(x) = x g(x) = -x g(x) = x

10. No 15( pg 285) - 1 0 1 f(x) = x 3 Guide point

11. 5.4 Domain and Range Enter y Enter window Press graph Domain Range

12. STEP FUNCTION 1 2 3 4 5 6 7 5432154321 Range Domain

13. 5.5 Variation Direct Variation Two variables are directly proportional if the ratios of their corresponding values are always equal Gallons of gasoline Total Price Price /gallons 4$4.604.60/4 = 1.15 6$6.906.90/6= 1.15 8$9.209.20/8 = 1.15 12$13.8013.80/12 = 1.15 15$17.2517.25/15 = 1.15 The ratio = total price /number of gallons 5 10 15 20 10

14. Other Type of Direct Variation General equation, y = f(x) = kx n y= kx 3 K > 0 y = kx 2 K> 0 = kx K> 0 Inverse Variation y = n where k is positive constant and n> 0 y is inversely proportional to x n

15. No 4, Ex 5.5 ( pg 309) The force of gravity( F ) on a 1-kg mass is inversely proportional to the square of the object’s distance (D) from the center of the earth F F= k/d 2 ( k = constant of proportionality) a) Fd 2 = k = 9.8(1) 2 K = 9.8 b) F= 9.8/d 2 substitute k 2 124 9.82.450.6125 Distance Earth Radii Force (Newtons) 1 2 3 4 5 Distance d 86428642 Force Graph

16. Pg 311, No 11 The weight of an object on the moon varies directly with its weight on earth a) m w where m = weight of object, on moon and w= wt. Of object on earth m = kw m = 24.75 pounds, w = 150 pounds K = 24.75/150 = 0.165 m = 0.165w, substitute k b) m = 0.165( 120) = 19.8 pounds c) w= m/k = 30/0.165 = 303.03 pound w100150200400 m16.524.753366 Wt. on moon (m) Wt. on earth (W) d)

17. Functions as Mathematical Models (Shape of the graph) Time Elapsed Distance from Home walk wait bus

18. Example 5, Pg 322 Gas Station Mall Highway 17 15 miles Miles in highwa y 051015202530 Miles from Mall 1510505 15 10 20 30 Miles in Highway 15 10 5 Miles from Mall f(x)= - x + 15 x - 15 When 0 < x < 15 When x > 15

19. 0 10 20 30 10 < x < 20 x – 15 < 5 15 10 5 0 10 20 30 15 10 5 Miles on highway Miles from Mall x – 15 > 10 The solution is x 25 x y x y Pg 323