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Holt Algebra 1
4-3 Writing Functions
Writing Functions
4-3
Holt Algebra 1
4-3 Writing Functions
Example 1: Using a Table to Write an Equation
Determine a relationship between the x- and y-values. Write an equation.
x
y
5 10 15 20
1 2 3 4
Step 1 List possible relationships between the first x and y-values.
5 – 4 = 1 and
Holt Algebra 1
4-3 Writing Functions
Example 1 Continued
Step 2 Determine which relationship works for the other x- and y- values.
10 – 4 2 and
15 – 4 3 and
20 – 4 4 and
The value of y is one-fifth, , of x.
Step 3 Write an equation.
or The value of y is one-fifth of x.
Holt Algebra 1
4-3 Writing Functions
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- and y-values.
1 3 = 3 and 1 + 2 = 3
Holt Algebra 1
4-3 Writing Functions
y = 3x
Check It Out! Example 1 Continued
Step 2 Determine which relationship works for the other x- and y- values.
2 • 3 = 63 • 3 = 94 • 3 = 12
2 + 2 6 3 + 2 9 4 + 2 12
The value of y is 3 times x.
Step 3 Write an equation.
The value of y is 3 times x.
Holt Algebra 1
4-3 Writing Functions
The input (x-values) of a function is the independent variable. The output (y-values) 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
4-3 Writing Functions
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
Holt Algebra 1
4-3 Writing Functions
Identify the independent and dependent variablesin the situation.
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.
Example 2B: Identifying Independent and Dependent Variables
Holt Algebra 1
4-3 Writing Functions
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
4-3 Writing Functions
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
4-3 Writing Functions
The dependent variable is a function of the independent variable.
y = f(x)
Holt Algebra 1
4-3 Writing Functions
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.
Example 3A: Writing Functions
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
4-3 Writing Functions
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
4-3 Writing Functions
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
Holt Algebra 1
4-3 Writing Functions
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
4-3 Writing Functions
Write a function to describe the situation. Find a reasonable domain and range for the function.
Ex. 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}
Holt Algebra 1
4-3 Writing Functions
H Dub• 4-3 Pg. 218 #11-15, 33-36, 40-45