1. Scuba diver a scuba diver dives straight down into the water quantities: the depth of the dive the water pressure on the diver

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Godfrey Watts
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1 HW - Functions and Rates name in #1-10, several situations are given below. for each, answer the following questions: a) does one quantity depend on another? if so, how? b) if the answer to (a) is yes, sketch a rough graph. label the axes. 1. Scuba diver a scuba diver dives straight down into the water quantities: the depth of the dive the water pressure on the diver 2. walking to school some friends walk to class together quantities: the time it takes to walk to class the number of people walking 3. falling egg an egg is dropped from a tenth story window quantities: the length of time the egg has fallen the distance the egg has fallen 4. paycheck a person works at a part-time job for an hourly wage quantities: the amount of the person's weekly paycheck the number of hours the person works in a week 5. carpool some people carpool to work quantities: the amount each person spends on gas the number of people who carpool 6. cooling tea a cup of hot tea is put on a table in a cold room for a long time quantities: the temperature of the drink the amount of time it has been on the table 7. paint crew a crew of painters paints a house quantities: the time it takes to paint the house the number of people in the crew

2 8. gas in a tank a person takes a car on a trip quantities: the amount of gas in the tank the total distance that can be driven 9. draining a swimming pool water drains from a swimming pool quantities: the water level in the pool the volume of water in the pool 10. symphony an orchestra plays a symphony quantities: the number of people in the orchestra how long it takes to play the symphony 11. A farmer has 1000 yards of fence to use to make a rectangular corral. Let x be the length of the corral. He wants to know how much Area he will enclose. a. Explain why A(x) = x(500 - x) is an algebraic representation for this situation. b. Sketch and label a graph of A; be sure to label the axes. c. Show that (100, 40000) is a point on the graph of y = A(x). What meaning do these coordinates have for this problem? d. What is the largest area of rectangular corral that can be built? Indicate the point on the graph that represents the maximum area.

3 12. Let f(x) = x 2 + 3x - 4. here is the graph: a. The domain of f is: b. The range of f is: c. f(-3) = d. f(2.2) = e. For what values of x does f(x) = 3? f. For what values of x does f(x) = 0? g. For what values of x is x 2 + 3x - 4 > 0? h. Which representation, the graph or the equation, of the function f did you use to answer parts (a)- (g) above, and why did you use that representation? 13. the graph below shows the height of a weather balloon over time, starting from when it was launched. approxiamtely how high was the balloon 20 seconds after launch? at what time as the balloon at a height of 20 feet? what change in height occurred between 20 and 30 seconds after launch? during what period was the balloon rising? tell a story of the flight of the balloon that matches the graph.

4 14. below is a graph showing the number of fish of a particular species in a lake over 100 days. P stands for population, the number of fish t stands for time, the number of days since the beginning of the observation approximately how many fish were there in the lake on day 40? when was the population level about 800 fish? estimate the change in the fish population between day 20 and day 40 when was the population increasing the fastest? Describe in words how this fish population grew over the first 100 days? 15. On a long trip beginning at 12pm, a driver recorded the following times and distances: time total distance (miles) 2pm 130 5pm 325 7pm 445 8pm 510 did the driver go the same speed for the entire trip? How do you know? What can you say about the driver's speed between 12pm and 5pm? What about the speed at 4pm?

16. a) who grew faster between age 10 and age 15? b) at what age was Paul growing the fastest? c) was Paul growing faster at age 7 or age 10? c) estimate his growth rate at age 15. 17.

5 16. a) who grew faster between age 10 and age 15? b) at what age was Paul growing the fastest? c) was Paul growing faster at age 7 or age 10? c) estimate his growth rate at age a truck in New York drove 280 miles in 4 hours. at this point, the truck crossed the state line into Connecticut. then it continued for a half-hour traveling 35 miles before stopping. what was different about the truck's travels in each state? what was the same? 18. this graph shows the distance traveled by a car on a trip from NYC to Boston. did the car travel the same speed the whole trip? what was the average speed for the trip?

6 19. a car is racing down a road. Below is a table of times and how far the car had traveled at that time. How fast is the car traveling at the 2 second mark? Is your answer exact or approximate? Time Distance (seconds) (feet)

1ACE Exercise 4. Name Date Class

1ACE Exercise 4. Name Date Class 1ACE Exercise 4 Investigation 1 4. A farm wants to add a small rectangular petting zoo for the public. They have a fixed amount of fencing to use for the zoo. This graph shows the lengths and areas of