Lesson 4.3 Writing Functions

Lesson 4.3 Writing Functions

Learning goals:

• I can identify independent and dependent variables. 

• I can write an equation in function notation and evaluate a function for given input values.

Vocab:

• Independent Variable: input of the function (x)

• Dependent Variable: output of the function (y)

Example 1

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

Multiple Choice

Write the function rule for the following table.

•  5x
• 5x + 1
•  x + 5
•  x + 1

Example 2A:

Identify the independent and dependent variables in each situation.

In the winter, more electricity is used when the temperature goes down, and less is used when the temperature rises.

Example 2B:

Identify the independent and dependent variables in each situation.

The cost of shipping a package is based on its weight.

Example 2B:

Identify the independent and dependent variables in each situation.

The faster Ron walks, the quicker he gets home.

Multiple Choice

On a graph, which axis shows the independent variable?

• x-axis
• y-axis
• neither
• it changes

Multiple Choice

On a graph, which axis shows the dependent variable?

• x-axis
• y-axis
• neither
• it changes

Multiple Choice

In the table, Bubbles is the ______________.

• independent variable

• dependent variable

Multiple Choice

Name the INDEPENDENT variable from the table below.

• words
• minutes

Vocab:

• Function Rule: an algebraic expression that defines a function (fancy word for equation)

• Function Notation: f(x) - (same as y)

Example 3A:

Identify the independent and dependent variables.  Write a rule in function notation for each situation.

A lawyer’s fee is $200 per hour for her services.

Example 3B:

Identify the independent and dependent variables. Write a rule in function notation for each situation.

The admission fee to a local carnival is $8.  Each ride costs $1.50.

Multiple Choice

A pizzeria charges $12 per pizza plus an additional $3 for delivery. Which equation represents the cost of having any number of pizzas delivered?

• c = 12p + 3
• c = 12p
• c = 3p
• c = 12 + 3p

Example 5:

(yes we skipped 4, you will get it later)

Manuel has already sold $20 worth of tickets to the school play.  He has 4 tickets left to sell at $2.50 per ticket.  Write a function rule to describe how much money Manuel can collect from selling tickets.  Find a reasonable domain and range for the function.