*Unit 5 Transformations Ch. 4 Functions, Relations & Transformations 4.1 Interpreting Graphs p Function Notation p Lines in Motion p Translations & Quadratics p Reflections & Square Roots p Dilations & Absolute Values p Transformations & Circles p Compositions of Functions p.237 *Unit 3 Polynomials & Quadratics = Ch. 7 *Unit 4 Conic Sections = Ch. 8

Ch. 4.1 Interpreting Graphs Objectives: Interpret graphs that show information about real-world situations Make a graph that reflects information in a story Invent a story that conveys the information in a graph

Vocabulary Independent variable: x-values Dependent variable: y -values Discrete graphs: graphs made of isolated points (ex. sequences – b/c the term # (n) must be a whole number) Continuous graphs: points are all connected (domain is the set of Real #’s) If you owned a hair cut salon, how would you determine the cost of a haircut?

Ex.) Customers: Haircut Price What is the real-world meaning of the slope of this graph? What does the x-intercept represent? What does the y-intercept represent?

Ex.) Customers: Haircut Price ANSWERS The number of customers depends on the haircut $. Independent variable: the dollar price of a haircut Dependent variable: # of customers Linear Relationship: y = mx + b As the price increases, the number of customers decreases. Slope (m): indicates the number of customers lost for each dollar increase. x-intercept: the haircut price that is too high for anyone. y-intercept (b): the number of customers when haircuts are free.

Ex.2.) Vending Machine Situation Students at Reagan IB HS are complaining that the juice vending machine is frequently empty. Several student council members decide to study this problem. Justify each answer. a.) Based on the graph, at what times is juice consumed most rapidly? b.) When is the machine refilled? c.) When is the machine empty? d.) Solutions?

Ex.2.) Vending Machine ANSWERS a.) The most rapid consumption is pictured by the steep, negative slopes from 11:30am to 12:30pm & 3 – 3:30pm. b.) The machine is completely refilled overnight, again at 10:30am & again just after school lets out. The machine is also refilled at 12:30pm, but only to 75% capacity. c.) The machine is empty from 3:30 – 4pm, and briefly at about 12:30pm. d.) Solution: Refill the machine once more at about 2 or 3pm. OR: Refill the machine completely at 12:30pm.

Investigation: p.186 Let x = time (hours) and y = water level (inches)

Investigation Part 2: p.186

Possible Solns. Part I: Part II: You have a small outdoor swimming pool. Your cousins want to use the pool, but the water level is very low. You turn on the hose and fill at a constant rate. Your cousins become impatient, so you increase the water flow to fill the pool faster. When the pool is completely full, you turn off the hose. Your cousins are careful not to splash water out of the pool. After they get out, you begin to empty the pool. The water pours out rapidly at first, then more slowly as there is less and less water left. You leave just a little water in the bottom, which will slowly evaporate. Time (min.)

Interpreting Graphs Summary Real WorldGraph Growing Shrinking Unchanged Increasing Decreasing Horizontal Discrete Continuous Separated points Connected points Linear Nonlinear Straight line Curved Independent variable Dependent variable Horizontal axis (x) Vertical axis (y)

Practice: Ch. 4 Practice Packet p.19 Lesson 4.1 Interpreting Graphs #(1-4)