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,

FunctionsMA.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

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.

1. Understand the concept of a function and use function notation.

F-IF Interpreting Functions

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.

2. Interpret functions that arise in applications in terms of the context.

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?

Grade 8 MA.8.A.1.6 Sample Item 63 MC

Does this graph represent a function?

MA.912.A.2.4

Sample Item 3

1. The quantity of gasoline consumed in the U.S.

is a function of the price per gallon.

a. Does this curve appear to have a positive slope or a negative slope?

b. Why do you suppose this is the case?

2. 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 slopesmore steeply upward as time increases?

b. What are the domain and range of this function?

3. The height above the ground of a cannon ball shot from a cannon is a function of the time since it was shot.

a. When the time equals 0, why is the height of the cannon ball not equal to 0?

b. Write a statement to describe the domain.

c. Write a statement to describe the range.

4. The profit from a restaurant is a function of the number of meals that are served.

a. Why does the range of this function include negative values?

b. What is the significance of the point (x-intercept) where the line crosses the horizontal axis?

5. The cost per month of owning a car is a function of the number of miles driven.

a. When the number of miles driven equals 0, why is the cost per month not equal to 0?

b. Why does the graph have a positive slope?

6. The temperature in an oven set at 350 degrees Fahrenheit is a function of the time since it was turned on.

a. When time equals 0, why is the temperature in the oven not equal to 0?

b. Why does the temperature eventually oscillate around 350 degrees Fahrenheit?

7. The time it takes to ride a bicycle 100 miles is a function of the average speed.

a. How long does it take to ride 100 miles at 5 mph? 10 mph? 15 mph? 20 mph? 25 mph? 35 mph?

b. Does the domain of this function include 0 mph?Explain why or why not.

8. The cost of postage for a first-class letter is a function of its weight in ounces.

a. 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?

$0.25

$1.00

$1.50

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.

Make a sketch for each function described below.Use your knowledge of the relationship described