3.7 Lesson on Functions and Dependent/Independent Variables

What is a Function?

​A function is a relation where each input (x) has exactly one output (y).

To test whether a relation is a function:

When given ordered pairs, if the x values repeat, it is NOT a function​.

When given a graph, use the vertical line test. ​If a vertical line intersects a graph more than once, it is NOT a function.

Examples:

​The x values repeat,

so it is NOT a

function.​The input 3

has an output of 5 and

an output of 3.​

​

Is it a function?

​

{(5,-2), (3,-5), (2,-5), (0,-2), (-1,-3)}

​

The x values do not repeat, so this IS a function.​

Is it a function?

If you place a vertical line at x=1, it wll pass through 2 points, so this is NOT a function.

​Is it a function?

​Try It!

Determine if each relation is a function.

Multiple Choice

Is it a function?

• Yes

• No

Multiple Choice

Is it a function?

• Yes

• No

Multiple Choice

Is it a function?

• Yes

• No

Multiple Choice

Is it a function?

• Yes

• No

Multiple Choice

Is it a function?

• Yes

• No

Multiple Choice

Is it a function?

• Yes

• No

Multiple Choice

Is it a function?

• Yes

• No

Multiple Choice

Is it a function?

• Yes

• No

Multiple Choice

Is it a function?

• Yes

• No

Multiple Choice

Is it a function?

• Yes

• No

Multiple Choice

Is it a function?

• Yes

• No

Multiple Choice

Is it a function?

• Function

• NOT a Function

Multiple Choice

Is it a function?

• Function

• NOT a Function

Multiple Choice

Is it a function?

• Function

• NOT a Function

Multiple Choice

Is it a function?

• Function

• NOT a Function

Dependent and INdependent VARIABLES

By Jennifer Mackie

In any situation, it is the variable affected or the result of changes by another factor.

It is found on the y axis​.

​

​What do you depend on?

​Dependent

Variable​

​

This is the cause of the action. It is found on the x axis .

​

​INdependent

Variable​

​

The height (h) of a plant and the amount of water (w) it receives.

• What is the independent variable?

• What is the dependent variable?

The height (h) of a plant and the amount of water (w) it receives.

• Independent variable - w

• Why?

• Water is the independent variable because it will change the height of the plant by helping it grow.

The height (h) of a plant and the amount of water (w) it receives.

• Dependent variable - h

• Why?

• The height is the dependent variable because the independent variable (water) caused the plant to change (grow).

Now It Is Your Turn!

Ask yourself: What causes (independent variable) and what changes (dependent variable)?

Multiple Select

The pages (p) in a book and the weight (w) of the book

• Independent variable - p

• dependent variable - p

• Independent variable - w

• dependent variable - w

Multiple Select

The pounds (p) pf flour you buy and the number of bread loaves (l) you can make

• Independent variable - l

• Independent variable - p

• Dependent variable - l

• Dependent variable - P

Multiple Select

The number of hamburgers (h) sold and the dollar amount of sales (s) taken in

• Independent variable - s

• Independent variable - h

• Dependent variable - h

• Dependent variable - s

Multiple Select

The temperature (t) of water and the number of minutes (m) the water is in the freezer

• Independent variable - m

• Independent variable - t

• Dependent variable - m

• Dependent variable - t

Multiple Choice

On a graph, which axis shows the independent variable?

• x-axis

• y-axis

• neither

• it changes

Multiple Select

The number of hours (h) worked and the amount of money (m) earned

• Independent variable - m

• Independent variable - h

• Dependent variable - h

• Dependent variable -

Multiple Choice

On a graph, which axis shows the dependent variable?

• x-axis

• y-axis

• neither

• it changes

Multiple Choice

Which of the following is the label for the independent variable?

• Money Collected

• Raising Money

• Boxes Sold

• None of the above

Multiple Choice

Name the INDEPENDENT variable from the table below.

• words

• minutes

Multiple Choice

Which label best describes the independent quantities shown in the table?

• Number of tickets (t)

• Cost (c)