# Section 2

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Section 2: Functions: Meaning, Notation, and Graphing « Introductory Example « Definition and Notation « Graphing a Function » Linear Cost Model
Introductory Example Fill the Gas Tank Your gas tank holds 12 gallons, but right now you're running on empty. As you pull into the gas station, the engine sputters and dies—the gas tal:lk is completely empty. You pump 12 gallons into the tank and swipe your credit card. How much does it cost? That depends on the price of gas, of course! But exactly how does it depend on the price? If the price per gallon is \$3.40, what is the cost to fill the tank? 17.-%.407°40.80 \$40. 70 If the price per gallon is \$4.10, what is the cost to fill the tank? 12-4.10 = 449.2.0 \$49.20 Fill the Gas Tank: Function and Symbolic Form The symbolic form: Write an algebraic expression for the cost price. In our example: to the consumer in terms of the =1 meF%:lr% This is read as: function of the price p per gallon. The cost, K(p), t0 fill the tank is a Written form: of \$3.40 per gallon is \$40.80." «"The cost of filling the tank at a price e ho hQQd For Uhits Symbolic form: k(3.40)=_40-80 36
< Practice Translating Statements Between Symbolic Form and Function Notation Here are some other examples from the gas tank situation: Words: At a price of \$2.00 per gallon, it costs \$24.00 to fill the tank. Write the symbolic form: ¥(2.00) =24 00 Words: The cost to fill a 1 2-gallon tank at a price of p dollars per gallonis 12 times p. Write the symbolic form: F(p) " [2-p Words: What is price per gallon if it costs \$45.00 to fill the tank? - D Symbolic form: What is p if K(p) = 45.00? Solve 12p = 45.00 for p. (We Il do this later.) "(P 12-P P35 price ber galithid 2P § 315, 37 \l V2 Evaluate a Function Evaluate the function K(p) = 12p at p = 3.50. Plug p = 3.50 into the expression 12p. Given the input p = 3.50, determine the output K(p). K(3.50) = 12 x 3.50 = \$42.00 Evaluate the function K(p) =12pat p=4.00 K(4)=12-4 - Evaluate the function K(p) = 12p at p = 3.50 Evaluate the function K(p + 1) = 12( P v | )=