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Chapter 2 Functions and Linear Functions

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§ 2.1 Introduction to Functions

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Blitzer, Intermediate Algebra, 4e – Slide #3 Basic FunctionsEXAMPLE SOLUTION Determine whether the following is a function guitar violin drums flute Yes, because none of the members of the domain correspond to more than one member of the range. DomainRange

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Blitzer, Intermediate Algebra, 4e – Slide #4 Basic FunctionsEXAMPLE SOLUTION Determine whether the following is a function beetles crickets ants moths No, because one of the members of the domain, 9, corresponds to more than one member of the range. DomainRange

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Blitzer, Intermediate Algebra, 4e – Slide #5 Basic FunctionsEXAMPLE SOLUTION Find the indicated function value: Replace x with 3 Evaluate the exponent Multiply Add and Subtract

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Blitzer, Intermediate Algebra, 4e – Slide #6 Basic FunctionsEXAMPLE SOLUTION Find the indicated function value: Replace z with -4 Evaluate the exponents Multiply Add

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Blitzer, Intermediate Algebra, 4e – Slide #7 Basic FunctionsEXAMPLE SOLUTION Find the indicated function value: Replace w with x+y Rewrite exponent Multiply Add Distribute NOTE: THIS CANNOT BE SIMPLIFIED ANY FURTHER!!!

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Blitzer, Intermediate Algebra, 4e – Slide #8 Graphing FunctionsEXAMPLE SOLUTION Graph the function. xy = -3x+1Ordered Pair (x,y) -2f(x) = -3(-2) + 1 = = 7(-2,7) f(x) = -3(-1) + 1 = = 4(-1,4) 0f(x) = -3(0) + 1 = = 1(0,1) 1f(x) = -3(1) + 1 = = -2(1,-2) 2f(x) = -3(2) + 1 = = -5(2,-5)

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Blitzer, Intermediate Algebra, 4e – Slide #9 Graphing FunctionsCONTINUED

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Blitzer, Intermediate Algebra, 4e – Slide #10 The Vertical Line TestEXAMPLE Use the vertical line test to identify graphs in which y is a function of x. (a)(b)(c)

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Blitzer, Intermediate Algebra, 4e – Slide #11 The Vertical Line TestSOLUTION CONTINUED (a)(b)(c) y is a function of xy is not a function of xy is a function of x

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Blitzer, Intermediate Algebra, 4e – Slide #12 Graphs of FunctionsEXAMPLE The figure shows the cost of mailing a first-class letter, f(x), as a function of its weight, x, in ounces. Use the graph to answer the following questions.

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Blitzer, Intermediate Algebra, 4e – Slide #13 Graphs of Functions (a) Find f (3). What does this mean in terms of the variables in this situation? CONTINUED (b) Find f (4). What does this mean in terms of the variables in this situation? (c) What is the cost of mailing a letter that weighs 1.5 ounces? (d) What is the cost of mailing a letter that weighs 1.8 ounces?

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Blitzer, Intermediate Algebra, 4e – Slide #14 Graphs of FunctionsSOLUTION CONTINUED f (3) = This means that when a first-class letter weighs 3 ounces, postage costs 83 cents. (a) Find f (3). What does this mean in terms of the variables in this situation?

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Blitzer, Intermediate Algebra, 4e – Slide #15 Graphs of FunctionsCONTINUED f (4) = This means that when a first-class letter weighs 4 ounces, postage costs $1.06. (b) Find f (4). What does this mean in terms of the variables in this situation?

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Blitzer, Intermediate Algebra, 4e – Slide #16 Graphs of FunctionsCONTINUED f (1.5) = This means that when a first-class letter weighs 1.5 ounces, postage costs $0.60. (c) What is the cost of mailing a letter that weighs 1.5 ounces?

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Blitzer, Intermediate Algebra, 4e – Slide #17 Graphs of FunctionsCONTINUED f (1.8) = This means that when a first-class letter weighs 1.8 ounces, postage costs $0.60. (d) What is the cost of mailing a letter that weighs 1.8 ounces?

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Blitzer, Intermediate Algebra, 4e – Slide #18 Graphs of Functions Obtaining Information from Graphs A closed dot indicates that the graph does not extend beyond this point and the point belongs to the graph. An open dot indicates that the graph does not extend beyond this point and the point does not belong to the graph. An arrow indicates that the graph extends indefinitely in the direction in which the arrow points.

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Blitzer, Intermediate Algebra, 4e – Slide #19 Domain and RangeEXAMPLE Use the graph of the function to identify its domain and range.

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Blitzer, Intermediate Algebra, 4e – Slide #20 Domain and Range {x | x is a real number} SOLUTION {y | y 3.6} Domain = Range =

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