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# Draw the graphs of some step functions

For all define where denotes the greatest integer less than or equal to . Draw the function for each of the following on the interval :

1. .
2. .
3. .
4. 1. Graph of . 2. Graph of . 3. The graph of . 4. The graph of . 1. Anonymous says:

I think you shall define the value of function when x = 2.

2. Artemii says:

a) is wrong. For example h(-0.5) = [-0.5] + [-1] = 0 – 1 = -1.
In reality, the drawing will be like this:
h( -1 ) = -3;
h( (-1, 0.5] ) = -1;
h( (-0.5, 0] ) = 0;
h( (0, 0.5] ) = 2;
h( (0.5, 1] ) = 3;
h( (1, 1.5] ) = 5;
h( (1.5, 2] ) = 6.
(I hope such a record does not create difficulties)

• Artemii says:

I’m sorry, it’s not. My function is the smallest integer >= x

3. sigh says:

c) is wrong. Note that ceil(0) * ceil(anything) = 0. So the interval [-1,0] on graph c should be 0.

• Anonymous says:

Let’s take x = -1/2 for instance. We have [x] = -1 and [2x] = -1. Therefore, h(x) = f(x)g(x) = 1

4. Artem says:

There is a mistake: the interval is closed on the right: you should also include the point at x=2 in the plots