Functions MA.8.A.1.6 Compare the graphs of linear and non-linear functions for real-world situations. MA.912.A.2.3 Describe the concept of a function, use function notation, determine whether a given relation is a function, and link equations to functions. MA.912.A.2.4 Determine the domain and range of a relation. MA.912.A.2.13 Solve real-world problems involving relations and functions.

F-IF Interpreting Functions Understand the concept of a function and use function notation. 1. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). 2. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.  

F-IF Interpreting Functions 2. Interpret functions that arise in applications in terms of the context.   4. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 5. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.

Grade 8 MA.8.A.1.6 Sample Item 63 MC In a certain city, the number of new houses built each month during the first half of the year decreased at a constant rate. During the second half of the year, the number of new houses built each month remained the same. Which graph best illustrates the number of houses built each month in this city?

Does this graph represent a function?

Sample Item 3 The book does not provide graphs like this MA.912.A.2.4

The quantity of gasoline consumed in the U.S. is a function of the price per gallon. 1. a. The curve appears to have a negative slope. b. As the price of gas increases the quantity consumed decreases because people cannot afford to buy as much. Additional questions: Why do you suppose the graph is not just a decreasing line? Do you think that the quantity would ever reach zero? Why does the curve seem to be leveling off? a. Does this curve appear to have a positive slope or a negative slope? b. Why do you suppose this is the case?

a. What scenario might explain why this curve slopes The distance from the starting line of a runner in the 100-meter dash is a function of the time since the start. a. What scenario might explain why this curve slopes more steeply upward as time increases? b. What are the domain and range of this function? 2. a. The runner probably starts out slow and then increases his speed as he gets closer to the finish line b. Domain from 0 sec to 11 sec Range from 0 meters to 100 meters

When the time equals 0, why is the height of the 3. The height above the ground of a cannon ball shot from a cannon is a function of the time since it was shot. When the time equals 0, why is the height of the cannon ball not equal to 0? Write a statement to describe the domain. Write a statement to describe the range. a. The cannon ball is shot from the height of the cannon, not the ground. The domain is the time the cannon was released to the time the cannon reached ground level. The range is from ground level (height = 0) to the highest point the cannon reached.

Why does the range of this function include negative values? 4. The profit from a restaurant is a function of the number of meals that are served. Why does the range of this function include negative values? What is the significance of the point (x-intercept) where the line crosses the horizontal axis? 4. a. The negative values are the cost involved in operating the restaurant, they must serve a certain number of meals to pay for operating costs. b. The x-intercept represents the number of meals that must be served to break even with the operating cost.

When the number of miles driven equals 0, why 5. The cost per month of owning a car is a function of the number of miles driven. When the number of miles driven equals 0, why is the cost per month not equal to 0? Why does the graph have a positive slope? 5. a. Whether you drive your car or not for a month, there might be other expenses such as insurance. b. The more miles you drive, the more the cost will increase- gas, tires, oil changes, etc.

When time equals 0, why is the temperature in the oven not equal to 0? 6. The temperature in an oven set at 350 degrees Fahrenheit is a function of the time since it was turned on. When time equals 0, why is the temperature in the oven not equal to 0? Why does the temperature eventually oscillate around 350 degrees Fahrenheit? 6. a. Before the oven is turned on, it is most likely just above room temperature, zero degrees Fahrenheit would be very cold (32 degrees F is freezing!) b. When the temperature in the oven goes above 350, the oven turns off, then the temperature will drop just below 350, and then turn on again.

How long does it take to ride 100 miles at 5 mph? 7. The time it takes to ride a bicycle 100 miles is a function of the average speed. How long does it take to ride 100 miles at 5 mph? 10 mph? 15 mph? 20 mph? 25 mph? 35 mph? Does the domain of this function include 0 mph? Explain why or why not. 7. a. 20 hours, 10 hours, 6hours 40min, 5 hours, 4 hours, approx 2.86 hours (2 hours 51 min) b. Since the distance is 100 miles you would need to find the time by dividing 100 by zero which is undefined.

What is the cost for a 2 oz letter? For 2.1 oz letter? 8. The cost of postage for a first-class letter is a function of its weight in ounces. $1.50 $1.00 $0.25 8. a. $0.50, $0.75 b. The price will remain the same for a certain interval of ounces, and then the cost increases by $0.25 for each interval after that. What is the cost for a 2 oz letter? For 2.1 oz letter? b. Why does the graph look like a series of steps?

Make a sketch for each function described below. Use your knowledge of the relationship described 9. At a fixed price per ounce, the cost of gold is a function of the number of ounces you buy.

Make a sketch for each function described below. Use your knowledge of the relationship described 10. The height of your head above the ground as you ride a Ferris wheel is a function of the time since you got on.

Make a sketch for each function described below. Use your knowledge of the relationship described 11. The total cost of operating a lemonade stand is a function of the amount of lemonade sold.

Make a sketch for each function described below. Use your knowledge of the relationship described 12. The profit from operating lemonade stand is a function of the amount of lemonade sold.

Make a sketch for each function described below. Use your knowledge of the relationship described 13. The amount of water in a pan on a burner that is turned on “high” is a function of the time since the burner was turned on.

Make a sketch for each function described below. Use your knowledge of the relationship described 14. The height of a ball that is dropped from a height of 10 feet is a function of the time since it was dropped.