This graph shows the relationship between time and

This graph shows the relationship between time and the depth of water in a leaky swimming pool. What is the dependent variable? Depth (ft) What is the independent variable? Time (hrs) a. What is the initial depth of the water? 2 feet b. For what time interval(s) is the water level decreasing? 2<x<6 11 < x < 16 c. What accounts for the decrease(s)? The pool’s leak d. For what time interval(s) is the water level increasing? 6 < x < 10 e. What accounts for the increase(s)? Filling the pool back up with water f. Is the pool ever empty? How can you tell? No because the depth never reaches zero feet.

This graph shows the volume of air in a balloon as it changes over time. a. What is the independent variable? How is it measured? Time, seconds b. What is the dependent variable? How is it measured? Volume, cubic inches c. For what time intervals is the volume increasing? What accounts for the increases? 2<x<4 5. 5 < x < 8 9 < x < 12

You Try! Given the graph of the distance from a Ranger’s station (in miles) while hiking in the Smokies. What is the dependent variable in this graph? Distance from the Rangers’ station in miles Using inequality notation, list the domain, range and when the function is increasing, decreasing, and constant: Domain Range Increasing Decreasing Constant What is the distance at 11 AM? 10 miles from the station Approximately how long will it take a hiker to be 8 miles away? 3 hours

Functions that have smooth graphs, with no breaks in the domain or range, are called continuous functions. Functions that are not continuous often involve quantities—such as people, cars, or stories of a building—that are counted or measured in whole numbers. Such functions are called discrete functions. Below are some examples of discrete functions. Describe each graph as increasing or decreasing at a constant or changing rate & continuous or discrete Decreasing @ changing rate, continuous Increasing @ constant rate, discrete Increasing @ changing rate, continuous Decreasing @ changing rate, discrete Increasing @ constant rate, continuous

Matching-Up Investigation Read the description of each situation below. Identify the independent and dependent variables. Then decide which of the graphs above match the situation. Time Tiger population Discrete, starting slightly above zero, increasing @ a changing rate Time Tea temperature Continuous, starting far up y-axis, decreasing @ a changing rate

Matching-Up Investigation Read the description of each situation below. Identify the independent and dependent variables. Then decide which of the graphs above match the situation. Time Number of daylight hours Discrete, starting slightly above zero, increasing @ a changing rate Time Height of a person above ground on ferris wheel Continuous, starting 10 feet on y-axis, increasing until it reaches it’s max, then starts decreasing back towards ground. Never touches x-axis.