# discrete vs. continuous

#### yeetet

##### New member
I am confused if this function is discrete or continuous because it is a rational function and it looks continuous but it has a removable discontinuity at -5 and it also has a vertical asymptote at 4 which makes me think it's not continuous but I don't think it's discrete either. I need help to know if this function is discrete or continuous.

Thanks for the help in advance!

#### tkhunny

##### Moderator
Staff member
Perhaps you could ponder the difference between "Everywhere Continuous" and just "Continuous".

Continuous EXCEPT at x= 4, maybe? I'm just guessing where that vertical asymptote is. I'm also just guessing about other characteristics, since you didn't manage to share the actual rational function with us.

Are you SURE this belongs in "Beginning Algebra"?

#### yeetet

##### New member
Sorry I forgot to share the function is this-

#### Dr.Peterson

##### Elite Member
I am confused if this function is discrete or continuous because it is a rational function and it looks continuous but it has a removable discontinuity at -5 and it also has a vertical asymptote at 4 which makes me think it's not continuous but I don't think it's discrete either. I need help to know if this function is discrete or continuous.
View attachment 26141
Thanks for the help in advance!
I wonder if you are confusing two different senses of the word "continuous" applied to functions. One, the sense in which this is "discontinuous", belongs formally to calculus, but can be mentioned in algebra. But that sense is not used in contrast to "discrete". The sense appropriate to your question relates to the nature of the domain. See here: