Answer to Question #218221 in Calculus for Ahmad

Question

Draw graphs of the following functions.

(a)

f: R—>R defined by f(x) = Floor(x)

(b)

f: R—>R defined by f(x) = Ceiling(x)

Answer 1

(a) The floor function is the function that takes as input a real number $x,$ and gives as output the greatest integer less than or equal to $x,$ denoted $Floor(x)$ or $\lfloor x \rfloor.$

(b) The ceiling function is the function that takes as input a real number $x,$ and gives as output the least integer greater than or equal to $x,$ denoted $Ceiling(x)$ or $\lceil x\rceil.$