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3-33-3 WritingWritingFunctionsFunctionsWarm UpLesson PresentationLesson QuizHolt1 Algebra 1HoltAlgebraMcDougal

3-3 Writing FunctionsWarm UpEvaluate each expression for a 2, b –3,and c 8.1. a 3c 262. ab – c –14c b 13. 124. 4c – b355. ba c17Holt McDougal Algebra 1

3-3 Writing FunctionsObjectivesIdentify independent and dependentvariables.Write an equation in function notation andevaluate a function for given input values.Holt McDougal Algebra 1

3-3 Writing FunctionsVocabularyindependent variabledependent variablefunction rulefunction notationHolt McDougal Algebra 1

3-3 Writing FunctionsExample 1: Using a Table to Write an EquationDetermine a relationship between the x- andy-values. Write an equation.x5y110 15 20234Step 1 List possible relationships between thefirst x or y-values.5 – 4 1 orHolt McDougal Algebra 1

3-3 Writing FunctionsExample 1 ContinuedStep 2 Determine if one relationship works for theremaining values.10 – 4 2and15 – 4 3and20 – 4 4andThe value of y is one-fifth,, of x.Step 3 Write an equation.orThe value of y is one-fifth of x.Holt McDougal Algebra 1

3-3 Writing FunctionsCheck It Out! Example 1Determine a relationship between the x- andy-values. Write an equation.{(1, 3), (2, 6), (3, 9), (4, 12)}x1234y36912Step 1 List possible relationships between thefirst x- or y-values.1 3 3 or 1 2 3Holt McDougal Algebra 1

3-3 Writing FunctionsCheck It Out! Example 1 ContinuedStep 2 Determine if one relationship works for theremaining values.2 3 63 3 94 3 122 2 63 2 94 2 12The value of y is 3 times x.Step 3 Write an equation.y 3xHolt McDougal Algebra 1The value of y is 3 times x.

3-3 Writing FunctionsThe equation in Example 1 describes a functionbecause for each x-value (input), there is only oney-value (output).Holt McDougal Algebra 1

3-3 Writing FunctionsThe input of a function is the independentvariable. The output of a function is thedependent variable. The value of thedependent variable depends on, or is afunction of, the value of the independentvariable.Holt McDougal Algebra 1

3-3 Writing FunctionsExample 2A: Identifying Independent andDependent VariablesIdentify the independent and dependent variablesin the situation.A painter must measure a room beforedeciding how much paint to buy.The amount of paint depends on the measurementof a room.Dependent: amount of paintIndependent: measurement of the roomHolt McDougal Algebra 1

3-3 Writing FunctionsExample 2B: Identifying Independent andDependent VariablesIdentify the independent and dependent variablesin the situation.The height of a candle decreases dcentimeters for every hour it burns.The height of a candle depends on the number ofhours it burns.Dependent: height of candleIndependent: timeHolt McDougal Algebra 1

3-3 Writing FunctionsExample 2C: Identifying Independent andDependent VariablesIdentify the independent and dependent variablesin the situation.A veterinarian must weigh an animal beforedetermining the amount of medication.The amount of medication depends on theweight of an animal.Dependent: amount of medicationIndependent: weight of animalHolt McDougal Algebra 1

3-3 Writing FunctionsHelpful HintThere are several different ways todescribe the variables of a bley-valuesDomainRangeInputOutputxf(x)Holt McDougal Algebra 1

3-3 Writing FunctionsCheck It Out! Example 2aIdentify the independent and dependentvariable in the situation.A company charges 10 per hour to rent ajackhammer.The cost to rent a jackhammer depends onthe length of time it is rented.Dependent variable: costIndependent variable: timeHolt McDougal Algebra 1

3-3 Writing FunctionsCheck It Out! Example 2bIdentify the independent and dependentvariable in the situation.Apples cost 0.99 per pound.The cost of apples depends on the numberof pounds bought.Dependent variable: costIndependent variable: poundsHolt McDougal Algebra 1

3-3 Writing FunctionsAn algebraic expression that defines a functionis a function rule. Suppose Tasha earns 5 foreach hour she baby-sits. Then 5 x is a functionrule that models her earnings.If x is the independent variable and y is thedependent variable, then function notation for yis f(x), read “f of x,” where f names the function.When an equation in two variables describes afunction, you can use function notation to write it.Holt McDougal Algebra 1

3-3 Writing FunctionsThe dependent variable is a function of theindependent variable.yisy a function offy f(x)Holt McDougal Algebra 1x.(x)

3-3 Writing FunctionsExample 3A: Writing FunctionsIdentify the independent and dependentvariables. Write an equation in function notationfor the situation.A math tutor charges 35 per hour.The fee a math tutor charges depends on numberof hours.Dependent: feeIndependent: hoursLet h represent the number of hours of tutoring.The function for the amount a math tutor charges isf(h) 35h.Holt McDougal Algebra 1

3-3 Writing FunctionsExample 3B: Writing FunctionsIdentify the independent and dependentvariables. Write an equation in function notationfor the situation.A fitness center charges a 100 initiationfee plus 40 per month.The total cost depends on the number of months,plus 100.Dependent: total costIndependent: number of monthsLet m represent the number of monthsThe function for the amount the fitness centercharges is f(m) 40m 100.Holt McDougal Algebra 1

3-3 Writing FunctionsCheck It Out! Example 3aIdentify the independent and dependentvariables. Write an equation in function notationfor the situation.Steven buys lettuce that costs 1.69/lb.The total cost depends on how many poundsof lettuce Steven buys.Dependent: total costIndependent: poundsLet x represent the number of pounds Steven buys.The function for the total cost of the lettuce is f(x) 1.69x.Holt McDougal Algebra 1

3-3 Writing FunctionsCheck It Out! Example 3bIdentify the independent and dependentvariables. Write an equation in function notationfor the situation.An amusement park charges a 6.00 parkingfee plus 29.99 per person.The total cost depends on the number of persons inthe car, plus 6.Dependent: total costIndependent: number of persons in the carLet x represent the number of persons in the car.The function for the total park cost isf(x) 29.99x 6.Holt McDougal Algebra 1

3-3 Writing FunctionsYou can think ofa function as aninput-outputmachine. ForTasha’s earnings,f(x) 5x. If youinput a value x,the output is 5x.Holt McDougal Algebra 1inputx 2functionf(x) 5x30output

3-3 Writing FunctionsExample 4A: Evaluating FunctionsEvaluate the function for the given input values.For f(x) 3x 2, find f(x) when x 7 andwhen x –4.f(x) 3(x) 2f(7) 3(7) 2 Substitute7 for x. 21 2Simplify. 23Holt McDougal Algebra 1f(x) 3(x) 2f(–4) 3(–4) 2 Substitute–4 for x.Simplify. –12 2 –10

3-3 Writing FunctionsExample 4B: Evaluating FunctionsEvaluate the function for the given input values.For g(t) 1.5t – 5, find g(t) when t 6 andwhen t –2.g(t) 1.5t – 5g(t) 1.5t – 5g(6) 1.5(6) – 5g(–2) 1.5(–2) – 5 9–5 –3 – 5 4 –8Holt McDougal Algebra 1

3-3 Writing FunctionsExample 4C: Evaluating FunctionsEvaluate the function for the given input values.For, find h(r) when r 600and when r –12. 202Holt McDougal Algebra 1 –2

3-3 Writing FunctionsCheck It Out! Example 4aEvaluate the function for the given input values.For h(c) 2c – 1, find h(c) when c 1and when c –3.h(c) 2c – 1h(1) 2(1) – 1h(c) 2c – 1h(–3) 2(–3) – 1 2–1 –6 – 1 1 –7Holt McDougal Algebra 1

3-3 Writing FunctionsCheck It Out! Example 4bEvaluate the function for the given input values.For g(t) , find g(t) when t –24 andwhen t 400. –5Holt McDougal Algebra 1 101

3-3 Writing FunctionsWhen a function describes a real-worldsituation, every real number is not alwaysreasonable for the domain and range. Forexample, a number representing thelength of an object cannot be negative,and only whole numbers can represent anumber of people.Holt McDougal Algebra 1

3-3 Writing FunctionsExample 5: Finding the Reasonable Domain andRange of a FunctionJoe has enough money to buy 1, 2, or 3 DVDsat 15.00 each, if he buys any at all.Write a function to describe the situation. Findthe reasonable domain and range of the function.Money spentf(x)is 15.00 15.00for each DVD.xIf Joe buys x DVDs, he will spend f(x) 15x dollars.Joe only has enough money to purchase 1, 2,or 3 DVDs. A reasonable domain is {0, 1, 2, 3}.Holt McDougal Algebra 1

3-3 Writing FunctionsExample 5 ContinuedSubstitute the domain values into the functionrule to find the range values.x0123f(x) 15(0) 0 15(1) 15 15(2) 30 15(3) 45A reasonable range for this situation is{ 0, 15, 30, 45}.Holt McDougal Algebra 1

3-3 Writing FunctionsCheck It Out! Example 5The settings on a space heater are the wholenumbers from 0 to 3. The total number of wattsused for each setting is 500 times the settingnumber. Write a function to describe the numberof watts used for each setting. Find thereasonable domain and range for the function.Number ofwatts usedis500wattsf(x) 500times the setting #.xFor each setting, the number of watts is f(x) 500x watts.Holt McDougal Algebra 1

3-3 Writing FunctionsCheck It Out! Example 5There are 4 possible settings 0, 1, 2, and 3, so areasonable domain would be {0, 1, 2, 3}.Substitute these values into the function rule to findthe range values.x0f(x)500(0) 01500(1) 5002500(2) 1,0003500(3) 1,500The reasonable range for this situation is {0, 500,1,000, 1,500} watts.Holt McDougal Algebra 1

3-3 Writing FunctionsLesson Quiz: Part IIdentify the independent and dependentvariables. Write an equation in functionnotation for each situation.1. A buffet charges 8.95 per person.independent: number of peopledependent: costf(p) 8.95p2. A moving company charges 130 for weeklytruck rental plus 1.50 per mile.independent: milesdependent: costf(m) 130 1.50mHolt McDougal Algebra 1

3-3 Writing FunctionsLesson Quiz: Part IIEvaluate each function for the given input values.3. For g(t) , find g(t) when t 20 andwhen t –12.g(20) 2g(–12) –64. For f(x) 6x – 1, find f(x) when x 3.5 andwhen x –5.f(3.5) 20f(–5) –31Holt McDougal Algebra 1

3-3 Writing FunctionsLesson Quiz: Part IIIWrite a function to describe the situation.Find the reasonable domain and range forthe function.5. A theater can be rented for exactly 2, 3, or 4hours. The cost is a 100 deposit plus 200per hour.f(h) 200h 100Domain: {2, 3, 4}Range: { 500, 700, 900}Holt McDougal Algebra 1

Holt McDougal Algebra 1 3-3 Writing Functions Example 5: Finding the Reasonable Domain and Range of a Function Write a function to describe the situation. Find the reasonable domain and range of the fu