Holt McDougal Algebra 1 3-3 Writing Functions Identify independent and dependent variables. Write an equation in function notation and evaluate a function

Holt McDougal Algebra 1

3-3 Writing Functions

Identify independent and dependent variables.

Write an equation in function notation and evaluate a function for given input values.

Objectives



Check It Out! Example 1

Determine a relationship between the x- and y-values. Write an equation.

{(1, 3), (2, 6), (3, 9), (4, 12)}

x

y

1 2 3 4

3 6 9 12

Step 1 List possible relationships between the first x- or y-values.

1 3 = 3 or 1 + 2 = 3



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.



Example 2A: Identifying Independent and Dependent Variables

Identify the independent and dependent variablesin the situation.

A 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




The height of a candle decreases d centimeters for every hour it burns.

Dependent: height of candle Independent: time

The height of a candle depends on the number of hours it burns.

Example 2B: Identifying Independent and Dependent Variables



A veterinarian must weigh 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


Example 2C: Identifying Independent and Dependent Variables



Helpful Hint

There are several different ways to describe the variables of a function.

IndependentVariable

DependentVariable

x-values y-values

Domain Range

Input Output

x f(x)



Check It Out! Example 2a

A company charges $10 per hour to rent a jackhammer.

Identify the independent and dependent variable in the situation.

The cost to rent a jackhammer depends on the length of time it is rented.

Dependent variable: costIndependent variable: time



Identify the independent and dependent variable in the situation.

Check It Out! Example 2b

Apples cost $0.99 per pound.

The cost of apples depends on the number of pounds bought.

Dependent variable: costIndependent variable: pounds



Identify the independent and dependent variables. Write an equation in function notation for the situation.

A math tutor charges $35 per hour.

The function for the amount a math tutor charges is f(h) = 35h.

Example 3A: Writing Functions

The fee a math tutor charges depends on number of hours.

Dependent: feeIndependent: hours

Let h represent the number of hours of tutoring.



A fitness center charges a $100 initiation fee plus $40 per month.

The function for the amount the fitness center charges is f(m) = 40m + 100.

Example 3B: Writing Functions


The total cost depends on the number of months, plus $100.

Dependent: total costIndependent: number of months

Let m represent the number of months





Steven buys lettuce that costs $1.69/lb.

The function for the total cost of the lettuce is f(x) = 1.69x.

The total cost depends on how many pounds of lettuce Steven buys.

Dependent: total costIndependent: pounds

Let x represent the number of pounds Steven buys.



Check It Out! Example 3bIdentify the independent and dependent variables. Write an equation in function notation for the situation.

An amusement park charges a $6.00 parking fee plus $29.99 per person.

The function for the total park cost is

f(x) = 29.99x + 6.

The total cost depends on the number of persons in the car, plus $6.

Dependent: total costIndependent: number of persons in the car

Let x represent the number of persons in the car.



You can think of a function as an input-output machine. For Tasha’s earnings, f(x) = 5x. If you input a value x, the output is 5x.

input

10

x

functionf(x)=5x

output

5x

6

30

2



Example 4A: Evaluating Functions

Evaluate the function for the given input values.

For f(x) = 3x + 2, find f(x) when x = 7 and when x = –4.

= 21 + 2

f(7) = 3(7) + 2 Substitute 7 for x.

f(x) = 3(x) + 2

= 23

Simplify.

f(x) = 3(x) + 2

f(–4) = 3(–4) + 2 Substitute –4 for x.Simplify.= –12 + 2

= –10



Example 4B: Evaluating Functions


For g(t) = 1.5t – 5, find g(t) when t = 6 and when t = –2.

g(t) = 1.5t – 5 g(t) = 1.5t – 5

g(6) = 1.5(6) – 5

= 9 – 5

= 4

g(–2) = 1.5(–2) – 5

= –3 – 5

= –8



Example 4C: Evaluating Functions


For , find h(r) when r = 600

and when r = –12.

= 202 = –2





For h(c) = 2c – 1, find h(c) when c = 1 and when c = –3.

h(c) = 2c – 1

h(1) = 2(1) – 1

= 2 – 1

= 1

h(c) = 2c – 1

h(–3) = 2(–3) – 1

= –6 – 1

= –7



Check It Out! Example 4b


For g(t) = , find g(t) when t = –24 and

when t = 400.

= –5 = 101



Lesson Quiz: Part I

Identify the independent and dependent variables. Write an equation in function notation for each situation.

1. A buffet charges $8.95 per person.independent: number of peopledependent: costf(p) = 8.95p

2. A moving company charges $130 for weekly truck rental plus $1.50 per mile.independent: milesdependent: costf(m) = 130 + 1.50m



Lesson Quiz: Part II

Evaluate each function for the given input values.

4. For f(x) = 6x – 1, find f(x) when x = 3.5 and when x = –5.

f(3.5) = 20f(–5) = –31

3. For g(t) = , find g(t) when t = 20 and

when t = –12.

g(20) = 2g(–12) = –6



Lesson Quiz: Part III

Write a function to describe the situation. Find the reasonable domain and range for the function.

5. A theater can be rented for exactly 2, 3, or 4 hours. The cost is a $100 deposit plus $200 per hour.

f(h) = 200h + 100Domain: {2, 3, 4}Range: {$500, $700, $900}

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Holt McDougal Algebra 1 3-3 Writing Functions Identify independent and dependent variables. Write an equation in function notation and evaluate a function