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

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!!)

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

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

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

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

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

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

Example 2: A jet airplane is flying at a rate of 280 miles per hour. Write a linear equation to express the distance traveled in a given amount of time. The distance traveled can be represented by __________________ = ________________ x _______________ DistanceRateTime 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

Time (hours)t Distance (miles)d Linear Equation: Dependent- distance Independent- time

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 equals 220 beats minus the person’s age r= 220 Since the ________ depends on the ______, then ______ is the independent variable. - a rate age

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

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

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