SECTION 5 2 INTERPRETING GRAPHS OF FUNCTIONS I

SECTION 5. 2 INTERPRETING GRAPHS OF FUNCTIONS

I) TERMS: DOMAIN AND RANGE Domain: All possible x-values (Input Numbers) that are allowed in a function Range: All possible y-values (Output Numbers) that are allowed in a function Ex: Find the Domain and Range: y 6 4 2 x -4 -3 -2 -1 0 -2 1 2 3 4 5 6 7 8 9

FIND THE DOMAIN AND RANGE FOR EACH GRAPH: y y 10 10 8 8 6 6 4 4 2 2 x x -5 -4 -3 -2 -1 0 1 2 3 4 5 -2 -2 The domain can be ‘All Real Number’

y 7 6 6 5 5 4 4 3 3 2 2 1 1 x 0 1 2 3 4 5 6 7

II) HOW TO READ GRAPHS Indicate what the X and Y axis represent X-axis: Dependent axis Y-axis: Independent axis Distance vs Time Speed vs Time, Quantity vs Time, …. Etc Understand what the slope represent Slope = Change in Vertical Distance Change in Horizontal Distance

EX: THE FOLLOWING GRAPH SHOWS JACK’S BANK ACCOUNTANT BALANCE FOR YEAR 2007. USE THE GRAPH TO ANSWER THE FOLLOWING QUESTIONS: y 1800 Balance($) 1600 Valentines Day Dad gives him money Halloween Fireworks Christmas Shopping 1400 1200 1000 800 600 400 200 Spends on his G. F. Works in Summer x Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan

QUESTIONS: When did he spend the most amount of money? From mid to late December, during Christmas When did he make the most amount of money? Early October, his dad gave him $1000 What does the y-intercept of the graph represent? How much money he had at the beginning of the year What does the slope of the line represent? If slope is going up How fast he’s making money If Slope is going down How fast he’s spending money

EX: A LITTLE GIRL RIDES HER BICYCLE UP A HILL. SHE GETS TO THE TOP AND THEN COAST DOWN THE HILL. DRAW A GRAPH FOR “HEIGHT VS TIME” & “SPEED VS TIME” Speed Height Fast Low Very Slow High Slowing down Going faster Fast Low y Height Speed y x x Time

EX: THE FOLLOWING GRAPH SHOWS JIMMY’S DISTANCE FROM HOME AS HE JOGS AROUND HIS NEIGHBOURHOOD. USE THE GRAPH TO ANSWER THE FOLLOWING QUESTIONS. y Distance (m) 5000 D 4000 E F C 3000 G B 2000 1000 H A 0 5 10 15 20 25 30 Time (minutes) 35 40 x 45

QUESTIONS: How fast was he running from A to B? He ran 2000 m in 5 minutes How fast was he running from B to C? He ran 1000 m in 5 minutes What happened from D to E? He was resting. He didn’t move further/closer to home What happened from G to H? How fast was he travelling? Tookwas the Bus home, distance couldn’t Travelled? run anymore What the total Just add all the vertical distance travelled: 8000 m

HOMEWORK: P 258 – 264 #1 - 10