Is it a function?

​DOMAIN & RANGE OF CONTINUOUS GRAPHS

For DOMAIN, scan your pencil from left to right along the x-axis.

​

For RANGE, scan your pencil from top to bottom along the y-axis.​

The domain is ALL REAL NUMBERS because the function will continue on both directions (left and right) forever.

​

The range is y ≥ −2 because the y-values cannot be less than −2.

​

Example:​

​

​Try It!

Find the domain and range of each relation.

Multiple Choice

Find the domain.

• $$x\ge-3$$  

• $$x\le3$$  

• $$-3\le x\le3$$  

Multiple Choice

Find the range.

• $$y\ge-3$$  

• $$y\le3$$  

• $$-3\le y\le3$$  

Multiple Choice

Find the domain.

• All Real Numbers 

•   $$x>7$$  

• $$x\le10$$   

Multiple Choice

Find the range.

• $$y\ge-10$$   

• All Real Numbers 

• $$y\le10$$   

Multiple Choice

Find the domain.

• All Real Numbers 

•   $$x\ge-2$$   

• $$x\le5$$    

Multiple Choice

Find the range.

• All Real Numbers  

• $$y\ge4$$   

•    $$y\le4$$  

Multiple Choice

Find the domain.

• All Real Numbers 

•     $$x\le-1$$  

• $$-1\le x\ge5$$     

Multiple Choice

Find the range.

• All Real Numbers  

• $$-3\le y\le3$$    

•    $$y\le4$$  

Multiple Choice

Find the domain.

• All Real Numbers 

•     $$x\ge-2$$   

• $$x\le0.5$$      

Multiple Choice

Find the range.

• All Real Numbers  

• $$-2\le y\le0.5$$     

•    $$y\le4$$  

Multiple Choice

Find the domain.

• All Real Numbers 

•     $$x\ge-3$$    

• $$x\le3$$       

Multiple Choice

Find the range.

• All Real Numbers  

• $$-3\le y\le2$$      

•    $$y\ge3$$   

Multiple Choice

Find the domain.

• All Real Numbers 

•     $$x\ge-3$$    

• $$x\ge-1$$        

Multiple Choice

Find the range.

• All Real Numbers  

• $$-3\le y\le2$$      

•    $$y\ge3$$   

Multiple Choice

Find the domain.

• All Real Numbers 

•     $$x=2$$     

• $$x\ge2$$         

Multiple Choice

Find the range.

• All Real Numbers  

• $$y=2$$       

•    $$y\ge3$$   

Multiple Choice

Find the domain.

• All Real Numbers 

•     $$x=4$$     

• $$x\ge-4$$         

Multiple Choice

Find the range.

• All Real Numbers  

• $$y=-4$$       

•    $$y\ge-4$$   

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?

• Yes

• No

Multiple Choice

Is it a function?

• Yes

• No

Multiple Choice

Is it a function?

• Yes

• No