Presentation on theme: "Warm Up Evaluate each expression for a = 2, b = –3, and c = 8."— Presentation transcript:
1Warm Up Evaluate each expression for a = 2, b = –3, and c = 8. 2. ab – c3.26–1412c + b14. 4c – b355. ba + c17
2Objectives Identify independent and dependent variables. Write an equation in function notation and evaluate a function for given input values.
3Vocabulary independent variable dependent variable function rule function notation
4The input of a function is the independent variable The input of a function is the independent variable. The output of a function is the dependent variable. The value of the dependent variable depends on, or is a function of, the value of the independent variable.
5Directions: Identify the independent and dependent variables in the situation.
6Example 1A painter must measure a room before deciding how much paint to buy.The amount of paint depends on the measurement of a room.Dependent: amount of paintIndependent: measurement of the room
7Example 2The height of a candle decrease d centimeters for every hour it burns.The height of a candle depends on the number of hours it burns.Dependent: height of candleIndependent: time
8Example 3A veterinarian must weight an animal before determining the amount of medication.The amount of medication depends on the weight of an animal.Dependent: amount of medicationIndependent: weight of animal
9Helpful HintThere are several different ways to describe the variables of a function.IndependentVariableDependentVariablex-valuesy-valuesDomainRangeInputOutputxf(x)
10Example 4A company charges $10 per hour to rent a jackhammer.The cost to rent a jackhammer depends on the length of time it is rented.Dependent variable: costIndependent variable: time
11Example 5Camryn buys p pounds of apples at $0.99 per pound.The cost of apples depends on the number of pounds bought.Dependent variable: costIndependent variable: pounds
12You can think of a function as an input-output machine. x2You can think of a function as an input-output machine.6functionf(x)=5x5x1030output
13Directions:Evaluate the function for the given input values.
14Example 6For f(x) = 3x + 2, find f(x) when x = 7 and when x = –4.f(x) = 3(x) + 2f(x) = 3(x) + 2Substitute7 for x.Substitute–4 for x.f(7) = 3(7) + 2f(–4) = 3(–4) + 2=Simplify.Simplify.= –12 + 2= 23= –10
15Example 7For g(t) = 1.5t – 5, find g(t) when t = 6 and when 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= –8
16Example 8For , find h(r) when r = 600 and when r = –12.= 202= –2
17Example 9For h(c) = 2c – 1, find h(c) when c = 1 and when c = –3.h(c) = 2c – 1h(c) = 2c – 1h(1) = 2(1) – 1h(–3) = 2(–3) – 1= 2 – 1= –6 – 1= 1= –7
18Example 10For g(t) = , find g(t) when t = –24 and when t = 400.= –5= 101
19Lesson Summary: Part IIdentify the independent and dependent variables.1. A buffet charges $8.95 per person.independent: number of peopledependent: cost2. A moving company charges $130 for weekly truck rental plus $1.50 per mile.independent: milesdependent: cost
20Lesson Summary: Part II Evaluate each function for the given input values.3. For g(t) = , find g(t) when t = 20 and when t = –12.g(20) = 2g(–12) = –64. For f(x) = 6x – 1, find f(x) when x = 3.5 and when x = –5.f(3.5) = 20f(–5) = –31