Unit 2 Functions

1. Unit 2 Functions Warm Up: Think of 2 things that depend on each other.

2. Everyday life… • plant growth depends on sunlight and rainfall • distance depends on rate of travel and time taken • voltage depends on current and resistance • test grades depend on attitude, listening in lectures and studying (among many other variables!!)

3. Functions • A function is a rule that relates how one quantity depends on other quantities • Example: • Distance= Rate X Time • If you drive fast, you go a longer distance • If you drive longer, you go a longer distance

4. Definitions Variable: quantity that can assume any given number • x, y, anything you can substitute a number into Constant: quantity that assumes to be unchanged • A number is already there…you can’t substitute another number in

5. Independent: x value: horizontal axis • Value determines other variables Dependent: y value: vertical axis • Value is determined by other variables

7. horizontal vertical On a graph, the independent variable is on the ________________ axis and dependent variable is on the _______________ axis. dependent independent

8. Remember Example 1?? The costs associated with being a member of a CD Club are presented in the table below.

9. From Example 1: xrepresented the number of CDs purchased and y represented the total cost Linear equations contain an independent variable and a dependent variable. independent dependent In this case x is called the ________________ variable and yis called the ________________________ variable. The total cost (y) depends on the number of CD purchased (x).

10. Write a linear equation to express the distance traveled in a given amount of time. Example 2: A jet airplane is flying at a rate of 280 miles per hour. The distance traveled can be represented by __________________ = ________________ x _______________ Distance Rate Time To find the ordered pairs (points) for the graph, make a table. Since distance depends on time, ________________ is the independent variable, and you can choose values for ___. time t

11. Linear Equation: 0 560 1120 1680 2240 2800 3000 2700 2400 2100 1800 Dependent- distance 1500 1200 900 600 Independent- time 300 2 4 6 8 10

12. Example 3: Exercise physiologists suggest that a reasonable estimate for the maximum heart rate during exercise is no more than 220 beats per minute minus the person’s age. Represent the maximum heart rate by r and the age by a. Write a linear equation to express the maximum heart rate (r) , in terms of age (a). Rate equals220 beatsminusthe person’s age - r = a 220 age Since the ________ depends on the ______, then ______ is the independent variable. rate age

13. Study examining if t.v. violence increases aggression in children. • Independent: TV watching Dependent: aggression in children B. Independent: aggression in children Dependent: TV watching C. Independent: the study Dependent: aggression in children

14. Are younger siblings treated better by their parents than older siblings? • Independent: treatment by parents Dependent: sibling status B. Independent: siblings’ gender Dependent: age of sibling C. Independent: sibling status Dependent: treatment by parents

15. Study predicting that high school sports build character • Independent: high school sports Dependent: character B. Independent: character Dependent: high school sports