Math Is Fun Forum

nycguitarguy

Member

Registered: 2024-02-24

Posts: 549

Domain & Range of Step Function

The step function aka greatest integer function is given below.

f(x) = int(2x)

Find the domain and range.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,198

Re: Domain & Range of Step Function

You'll see how this graph looks if you try some x values.

If x is 1 then 2x is 2 and int of that is still 2.

If x is 1.1, 1.2, 1.3, 2x is 2.2, 2.4, 2.6 and int of that is still just 2.

So this bit of the graph is a line straight across.

At 1.5 it changes 2x is 3 and int 3 is 3.

So the graph jumps up to a new line until x reaches 2 when it jumps up again. So you end up with a sort of staircase.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

nycguitarguy

Member

Registered: 2024-02-24

Posts: 549

Re: Domain & Range of Step Function

You'll see how this graph looks if you try some x values.

If x is 1 then 2x is 2 and int of that is still 2.

If x is 1.1, 1.2, 1.3, 2x is 2.2, 2.4, 2.6 and int of that is still just 2.

So this bit of the graph is a line straight across.

At 1.5 it changes 2x is 3 and int 3 is 3.

So the graph jumps up to a new line until x reaches 2 when it jumps up again. So you end up with a sort of staircase.

Bob

You said:

"At 1.5 it changes 2x is 3 and int 3 is 3."

So, 1.5 (2) = 3. We are simply multiplying, right?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,198

Re: Domain & Range of Step Function

No. This example yes, but not for other x inputs.

Eg f(1.2) = int(2.4) = 2

f(-4,6) = int(-9.2) = -10

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

nycguitarguy

Member

Registered: 2024-02-24

Posts: 549

Re: Domain & Range of Step Function

No. This example yes, but not for other x inputs.

Eg f(1.2) = int(2.4) = 2

f(-4,6) = int(-9.2) = -10

Bob

I am not sure how to find the domain of Step functions.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,198

Re: Domain & Range of Step Function

What values of x lead to a y value. Or are there any x values for which you cannot determine a y value.  If so exclude those from the domain.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

nycguitarguy

Member

Registered: 2024-02-24

Posts: 549

Re: Domain & Range of Step Function

What values of x lead to a y value. Or are there any x values for which you cannot determine a y value.  If so exclude those from the domain.

Bob

Let -00 = negative infinity

Let 00 = positive infinity

Domain = (-00, 00)

Range = (-00, 00)

I say x can be any integer.

I don't see a restriction.

I know very little about the step function.

You say?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,198

Re: Domain & Range of Step Function

The domain is good. Only integers are output from the function and then not all so you need to think some more about the range.

Try some values.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

nycguitarguy

Member

Registered: 2024-02-24

Posts: 549

Re: Domain & Range of Step Function

The domain is good. Only integers are output from the function and then not all so you need to think some more about the range.

Try some values.

Bob

Let me see what I can do at my end to understand the range.