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Name _____________________________ CoE: Using Function Notation 1. Raiden joins a gym, which offers memberships at a rate of $10 per month, with an initial signup fee of $25. The amount of money that he spends on the gym can be represented by the function 𝑓(𝑥) = 10𝑥 + 25, where 𝑥 represents the number of months that he has been a member of the gym and 𝑓(𝑥) represents the amount of money that he has spent in total. a. Complete the table by evaluating 𝑓(𝑥) for each value of x. Show your work here. b. 𝑓(2) = 45 is interpreted as “The value of the function is ____ when x is 2.” Number of months 𝑥 Amount of Money Spent 𝑓(𝑥) 0 1 2 3 4 5 6 Interpret: 𝑓(3) = 55: “The value of the function is ____ when the x is ___” 𝑓(5) = 75: “The value of the function is ____ when x is ___” c. For this situation, what does 𝑥 represent? What does 𝑓(𝑥) represent? d. So, in the context of the situation, we would interpret this way: 𝑓(2) = 45 is interpreted as “The amount of money spent is 45 when the number of months is 2.” Interpret: 𝑓(3) = 55: 𝑓(5) = 75: 2. Ashley buys a new guitar by making payments each month. The guitar originally costs $300 and she pays $20 each month. The amount of money that she still owes can be represented by the function 𝑓(𝑥) = 300 − 20𝑥, where x represents the number of months she has made payments and 𝑓(𝑥) represents the amount that she still owes. a. Complete the table of values by evaluating the function. Number of months 𝑥 b. What does x represent? What does 𝑓(𝑥) represent? Amount of Money owed 𝑓(𝑥) 0 1 2 3 4 5 6 c. What does the 300 represent in f(x) What does the -20 represent in f(x) d. Interpret: 𝑓(3) = 240: The amount of money owed is _____ when __________________________ is ______. 𝑓(10) = 100: The __________________________ is _______ when _______________________ is ___. 𝑓(6) =______ : The _________________________ is _______ when _______________________ is ___. e. What is the value of 𝑓(12)? f. What does the value of 𝑓(12) mean (for this situation)? g. Interpret: 𝑓(𝑥) = 260: The amount of money owed is _____ when __________________________ is ______. 𝑓(𝑥) = 200: The __________________________ is _______ when _______________________ is ___. 𝑓(𝑥) = 20 : The _________________________ is _______ when _______________________ is ___. h. Find the value of x that would make 𝑓(𝑥) = 260, AKA solve for f(x) = 260. i. Solve for f(x) = 20.