Evaluating A Step Function

The following examples are not from my textbooks.

I understand that for f(x) = [[ x ]], we round down if x is not an integer. I also know that f(x) is less than or equal to x.

Sample:

Evaluate g(x) = 3[[ x ]] for x = 2, x = 0.6, and x = -4.

Let x = 2

I know that 2 is an integer.

So, g(2) = 3[[ 2 ]] becomes 3(2) = 6.

Let x = 0.6

I know that 0.6 is not an integer. So, I must round down.

Number Line

<------(0)--------(0.6)---------(1)-------->

If I round down, the closes number on the line is 0.

So, g(0) = 3[[ 0 ]] = 3(0) = 0.

Let x = -4

I know that -4 is an integer. No need to round down.

So, g(-4) = 3[[ -4 ]] becomes 3(-4) = -12.

You say?

 

perfect!

 

I am going to finish this week evaluating step functions. There are 2 more questions with 4 parts that will be posted with work shown.