Diego said that these graphs are ordered from smallest to largest. Mai said they are ordered from largest to smallest. But these are graphs, not numbers! What do you think Diego and Mai are thinking?

1. Jada earns \$7 per hour mowing her neighbors’ lawns.
   1. Name the two quantities in this situation that are in a functional relationship. Which did you choose to be the independent variable? What is the variable that depends on it?
   2. Write an equation that represents the function.

   3. Here is a graph of the function. Label the axes. Label at least two points with input-output pairs.

      

2. To convert feet to yards, we multiply the number of feet by .
   1. Name the two quantities in this situation that are in a functional relationship. Which did you choose to be the independent variable? What is the variable that depends on it?
   2. Write an equation that represents the function.

   3. Draw the graph of the function.

      Label the axes and at least two points
      with input-output pairs.

      

There are four tanks of water.

• The amount of water in gallons, , in Tank A is a function of time in minutes, , and can be represented by the equation .
• The amount of water in gallons, , in Tank B is a function of time in minutes, . The amount of water starts at 400 gallons and is decreasing by 5 gallons per minute.

1. Which tank started out with more water?
2. Write an equation representing the relationship between and .
3. One tank is filling up. The other is draining out. Which is which? How can you tell?
4. The amount of water in gallons, , in Tank C is a function of time in minutes, , and can be represented by the equation . Is it filling up or draining out? Can you tell just by looking at the equation?

5. The graph of the function for the amount of water in gallons, , in Tank D at time is shown. Is it filling up or draining out? How do you know?

   

Noah is depositing money in his account every week to save money. The graph shows the amount he has saved as a function of time since he opened his account.  

Elena opened an account the same day as Noah. The amount of money in her account is given by the function , where  is the number of weeks since the account was opened.

1. Who started out with more money in their account? Explain how you know.

2. Who is saving money at a faster rate? Explain how you know.

3. How much will Noah save over the course of a year if he does not make any withdrawals? How long will it take Elena to save that much?

Scatterplot of Noah's account, horizontal, weeks since opening account, 0 to 12 by 2, vertical, amount in the account, 0 to 140 by 20. Points at 0 comma 60, 2 comma 70, 4 comma 80, 6 comma 90, 8 comma 100, 10 comma 110, 12 comma 120, and 14 comma 130.