Question

Graph f(x)=abs[x] (recall that [x] denotes the greatest integer function) and find the domain and range

Answer 1

Where do these go?

abs[1.5]
abs[0.5]
abs[-0.5]
abs[-1.5]

Answer 2

huh?

Answer 3

first off, what do they mean by the greatest integer function

Answer 4

That's what I was asking. There are various definitions. Often it is the "Greatest Integer NOT GREATER THAN the given value"

Therefore:

abs[1.5] = abs(1) = 1
abs[0.5] = abs(0) = 0
abs[-0.5] = abs(-1) = 1
abs[-1.5] = abs(-2) = 2

Make sense?

Answer 5

ok

Answer 6

but 1.5 is greater than 1

Answer 7

also i thought decimals are not integers

Answer 8

The Domain of this function is ALL Real Numbers.
The Range is quite a different animal.

The Greatest Integer function takes ANY argument but produces only integers. This, 1.5 can go into this function (no one cares if it's an integer), but you cannot get it out (it's not an integer).

Answer 9

what does the graph look like

Answer 10

and so how do we find the range

Answer 11

You tell me.

[0] = 0
[0.1] = 0
[0.2] = 0
[0.4] = 0
[0.8] = 0
[0.9] = 0
[0.99] = 0
[0.999] = 0
[0.9999] = 0
[0.99999] = 0
[1] = 1

Answer 12

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Answer 13

so is it just points on a graph

Answer 14

and range is just 0 and 1 and 2 and (no negatives)

Answer 15

No, it's mostly continuous. I just picked a few points between 0 and 1 to provide an example of it;'s behavior. Once you hit an integer, it jump to that integer and stays there until you hit the next integer.

Answer 16

can u draw it please

Answer 17

i am having trouble understanding you

Answer 18

It is a series of horizontal line segments. Start at (0,0) and proceed to (1,0). Traditionally, one uses a closed dot at (0,0) and an open circle at (1,0). Then it jumps to a closed dot at (1,1) and continues horizontally to an open dot at (2,1)

Answer 19

can you please draw it for me

Answer 20

Are you saying you cannot draw a horizontal line from (0,0) to (1,0)?

Answer 21

The closed circles on the left and closed on the right are missing, but that's the idea.