Question 1)
Convenience Store Your friends know that you stop at the local convenience store every morning on your way to school and get a bottle of juice. For your birthday, they get you a $50 gift card. Suppose that a small bottle of juice costs $2 and all you ever buy at the store is juice.1.(a)W rite a function, f, that can be used to track your gift card balance in terms of the number of bottles of juice, x, you have purchased.(b)What is the rate of change of this function? What does this mean for this scenario?(c)What will the graph of the function look like? How do you know?(d)What does )(=f“246” mean in the context of the problem?(e)Using the format given below, complete the table representing your function by choosing several different values representing the number of bottles of juiceyou have purchased and computing the remaining balance on your gift card. Then, use your table to construct ordered pairs of the form(xf,(x)).

Question 2)
Practice with Linear Functions For questions 1 and 2: Evaluate the function at the specified inputs for x. Write the input–output pairs in function notation and in a table of values. Graph each line by plotting the points you generated from the function.1.Consider the function given by fx()=-2x3. Use the tables below to determine the value of f at various x-values. Consider the function given by1gx()=+x12. Use the tables below to determine the values of g at various x-values.

Question 3)
write an algebraic function rule that can be used to model each scenario. Then explain what the slope and the vertical intercept mean in the context of the problem.7.At a local pumpkin patch you can pick your own pumpkins. There is a $5 chargeto enter the patch and then a $0.25 charge per pound of pumpkin. Let p representthe weight of the pumpkin you choose and Cp() represent the total cost of thepumpkin in terms of the weight of the pumpkin.8.You are skiing down a 1,350 meter ski slope at 60 meters per second. Let trepresent your skiing time in seconds and dt() represent the distance from thebottom of the ski slope.9.The basement of a building is 40 feet below ground level. The building’s elevatorrises at a rate of 5 feet per second. You enter the elevator in the basement. Let trepresent the number of seconds you are in the elevator and ht() represent howhigh the elevator has risen (in feet) in t seconds.10.There is a stack of old algebra books in the library. Each book is114inches thick .Let b represent the number of books in a stack and sb() represent the total height of the stack in inches.