Class,+Comp+and+Cont+Version+1+with+classmate+comments

//__Continuos Functions.__//
Difference between continuos functions and those that are not continuos, which are called discontinous functions, was enunciated in Bolzano’s Theorem, which postulated that if a function is continuos on an interval from //a// to //b//, when you calculate the output of //a// and //b//, then, all the possible values between f(//a//) and f(//b//) are outputs of of the number inside the interval.

There is not classification for continuos functions, but you can compare some characteristics between some of them, like trygonometrical, polynomials, exponential and logarithmic functions.


 * = Fuctions

Characteristics. ||= Trygonometrical functions ||= Inverse trigonometrical functions ||= Polynomial Functions ||= Exponential Function ||= Logarithmic Function || -1 to 1. ||= Defined for every real number ||= Defined for every real number ||= Defined for every possitive real number || So, talking about continuos functions we know: Commun characteristics: they are defined on intervals of real numbers, they take values on intervals too, they are differentiable, and there is always a primitive for them.
 * = On which intervals are they defined? ||= Defined for every real number. ||= Defined on the interval from
 * = Which values do they take? ||= They take values between -1 and 1 ||= They take values between 0 and 2∏ ||= They take values on every real number. ||= It takes values on every real number. ||= It takes values up to -1 and over. ||
 * = Do they take a minimun/ maximun value? ||= Yes, they can take a maximun and a minimun value. ||= Yes, they take maximun and minimun values. ||= They can take max/ min values or not, depending on the polynomial. ||= It take a min or max value depending on the variable (if it is possitive or no) ||= It takes a minimun value, but does not have a maximun one. ||

Particular Characteristics: :they can or can not have maximun or minimun values- depending on the function-, they can be defined over small intervals or for every real number, and sometimes there is an inverse function and sometimes there is not - depending on the function-.