linear equations

Question

When graphing a linear equation, what Is the difference between a circled point point of origin with a continuous line and one that's colored in?

Answer 1

An open point means the function is not defined AT THAT y value, for that value of x.

 

It could be defined for another y value, however.

 

 

2                     •------o

 

1            •------o

 

0   •------o

 

 

The is evident in the Greatest Integer Function (stair-step function), or piece-wise functions like the following.

 

 

f(x) = {  

 

2x + 4,   x> 0,

-x + 1    x < 0

 

}

 

 

Note that this function will be defined for every x EXCEPT 0.

 

You would have an open circle at the point (0, 4) for the first equation and one at (0, 1) for the second one.

 

 

Answer 2

Do you mean linear inequalities?  If so, then a filled-in point means that point is included whereas a circled point is not included.  As an example, the inequalities

 

x>1

 

x>=1

 

are both rays shooting off to the right from 1.  The first inequality does not include 1 while the second one does.  Hence the graph of the first will have an open circle at 1 and the graph of the second will have a filled-in circle at 1.