Introduction to Functions

Input and Output Values

Inputs

• Input of a function is the independent variable

• Also known as the domain or x values

Outputs

• Output of a function is the dependent variable. 

• Also known as the range or y-values

• You can also write y in function notation such as f(x)

Multiple Choice

Identify the independent and dependent variables

in the situation.

"A painter must measure a room before deciding how much paint to buy."

The amount of paint is the __________________.

• Dependent Variable

• Independent Variable

Multiple Choice

Identify the independent and dependent variables

in the situation.

"A painter must measure a room before deciding how much paint to buy."

The size of the room is the __________________.

• Dependent Variable

• Independent Variable

Multiple Choice

Identify the independent and dependent variables

in the situation.

"A veterinarian must weigh an animal before determining the amount of medication."

The weight of the animal is the __________________.

• Dependent Variable

• Independent Variable

Multiple Choice

Identify the independent and dependent variables

in the situation.

"A veterinarian must weigh an animal before determining the amount of medication."

The amount of medication is the __________________.

• Dependent Variable

• Independent Variable

Function Notation

An algebraic expression that defines a function is a function rule. Suppose Tasha earns $5 for each hour she baby-sits. Then 5 • x is a function rule that models her earnings.

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. 

Function Notation

• y          is     a function of         x. 

• y          =         f                       (x)

• y = f(x)

Multiple Choice

Identify the independent variable, dependent variable, and equation in function notation for the situation.

"A math tutor make $35 per hour"

• Independent: Hours Worked

  Dependent: Money Made

  Function: f(x)=35x

• Independent: Hours Worked

  Dependent: Money Made

  Function: f(x)=x+35

• Independent: Money Made

  Dependent: Hours Worked

  Function: f(x)=x+35

• Independent: Money Made

  Dependent: Hours Worked

  Function: f(x)=35x

Multiple Choice

Identify the independent variable, dependent variable, and equation in function notation for the situation.

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

• Independent: Total Cost

  Dependent: Number of Park Attendees

  Function:

  c(a) = 6+29.99a

• Independent: Total Cost

  Dependent: Number of Park Attendees

  Function:

  c(a) = 6a + 29.99a

• Independent: Number of Park Attendees

  Dependent: Total Cost

  Function:

  c(a) = 6+29.99a

• Independent: Total Cost

  Dependent: Number of Park Attendees

  Function:

  c(a) = 6a+29.99

Evaluating Functions

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.

To find f(x) when x = 3 you would replace x with 3 in the function.

f(x) = 5x

f(3) = 5(3)

f(3) = 15

Open Ended

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