Holt Algebra 1 4-3 Writing Functions Students will be able to: Identify independent and dependent variables and write an equation in function notation.

Holt Algebra 1

4-3 Writing Functions

Students will be able to: Identify independent and dependent variables and write an equation in function notation and evaluate a function for given input values.

Learning Target

Holt Algebra 1


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

x

y

5 10 15 20

1 2 3 4

1

5y x

5x 1y

linear

Holt Algebra 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 1x 3 6 9 12 3y

linear

3y x

Holt Algebra 1


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.

Holt Algebra 1


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

Holt Algebra 1



The height of a candle decrease 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.

Holt Algebra 1


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


Holt Algebra 1


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)

Holt Algebra 1


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

Holt Algebra 1


Identify the independent and dependent variable in the situation.

Camryn 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

Holt Algebra 1


An algebraic expression that defines a function is a function rule.

If x is the independent variable and y is the dependent variable, then function notation for y is f(x), read “f of x,” where f names the function. When an equation in two variables describes a function, you can use function notation to write it.

Holt Algebra 1


The dependent variable is a function of the independent variable.

y is a function of x.

y = f (x)

y = f(x)

Holt Algebra 1


Identify the independent and dependent variables. Write a rule 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.

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

Dependent: chargesIndependent: hours

Let h represent the number of hours of tutoring.

Holt Algebra 1


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.


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

Dependent: total costIndependent: number of months

Let m represent the number of months

Holt Algebra 1



Steven buys lettuce that costs $1.69/lb.

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

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

Dependent: total costIndependent: pounds

Let x represent the number of pounds Steven bought.

Holt Algebra 1



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.

Holt Algebra 1


You can think of a function as an input-output machine.

input

10

x

functionf(x)=5x

output

5x

6

30

2

Holt Algebra 1


2 1.5 2 5 3 5 8g

Evaluate the function for the given input values.

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

Evaluate the function for the given input values.

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

7 3 7 2 32 221f

4 3 4 2 12 12 0f

6 1.5 6 9 5 45g

Holt Algebra 1


When a function describes a real-world situation, every real number is not always reasonable for the domain and range. For example, a number representing the length of an object cannot be negative, and only whole numbers can represent a number of people.

Holt Algebra 1


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

Joe has enough money to buy 1, 2, or 3 DVDs at $15.00 each.

x y

1

2

3

15

30

45

15f x x : / 0,1,2,3,...

: / 0,15,30,45,...

D x x

R y y

Holt Algebra 1

4-3 Writing FunctionsThe settings on a space heater are the whole numbers from 0 to 3. The total of watts used for each setting is 500 times the setting number. Write a function rule to describe the number of watts used for each setting. Find a reasonable domain and range for the function.

Number of watts used

is 500 times the setting #.watts

f(x) = 500 • x

For each setting, the number of watts is f(x) = 500x watts.

HW pp. 249-251/13-23,25-31,36 : / 0,1,2,3

: / 0,500,1000,1500

D x x

R y y

Holt Algebra 1


Holt Algebra 1


Warm UpEvaluate each expression for a = 2, b = –3, and c = 8. 1. a + 3c

2. ab – c

3.

12 c + b

4. 4c – b

5. ba + c

26

–14

1

35

17

Holt Algebra 1


Solve the inequality and graph the solutions.

4

3

4

3

36g

9

3634 38

Holt Algebra 1 4-3 Writing Functions Students will be able to: Identify independent and dependent variables and write an equation in function notation.

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