Three QUICK questions about greatest integer functions.?

Question

I'm working with the function: f(x)= [[x]]. This is called a greatest integer function.

a) Does this function have symmetry? If so, what kind? I'm leaning toward origin symmetry, but i'm not sure at all.

b) Is this function even or odd?

c) Is this function considered "one-to-one'?

THANK YOU IN ADVANCE. Your help is greatly appreciated. thank you! :]

Answer 1

Do you know the graph of this function?

It is also called a step function as it looks like the steps of a ladder .. . .

see the graph of the 'floor function'

http://en.wikipedia.org/wiki/Greatest_in...

ok.

symmetry:

it will be symmetric wrt y-axis if there is a mirror reflection wrt y-axis.

thus it is not symmetric wrt y-axis. (This also implies the function is NOT even.)

it will be symmetric wrt x-axis if there is a mirror reflection wrt x-axis.

It wont be symmetric wrt x-axis as this is a function.

it will be symmetric wrt origin if for every point, there is another point such that the origin is their midpoint.

>> Now, given the point (0.5 , 0) , we know that (-0.5 , 0) is not on the graph.

Thus it is not symmetric wrt origin also.

The symmetry wrt origin also tells you that a function is an odd function.

Thus this function is neither odd nor even.

It would be one-to-one if it satisfies the horizontal line test.

From the graph, it is not one-to-one.

.. . .. .

Answer 2

Greatest Integer Function is a  function written as f(x) = [x], where f(x) is the greatest integer less than or equal to x.

I just have one [].

1) symmetry -- ??

2) even/odd -- no

not even f(50.1) is not = f(-50.1)

and

not odd because -f(10.5) is not = f(-10.5)

f(-10.5) in fact = -11

3) f(1.7) = 1 and f(1.6) = 1, so not one to one.

for two different x we have the same answer.