Question

Which graph represents the function on the interval [-3,3]
F(x)=[x]-2

Answer 1

Shown below

Explanation:

The most famous of the step functions is the greatest integer function, which is denoted by the parent function
`[x]`.

So, this function is defined as:

`f(x)=[x] \ the \ greatest \ integer \ less \ than \ or \ equal \ to \ x`.

These are the characteristics of this function:

• The domain of the function is the set of all real numbers.
• The range of the function is the set of all integers.
• The graph has a
  `y-intercept` at
  `(0,0)` and
  `x-intercept` in the interval
  `[0,1)`
• The graph is constant between each pair of consecutive integers.
• The graph jumps vertically one unit at each integer value.

The function
`F(x)=[x]-2` represents the parent function shifted 2 units downward. Therefore, the correct option has been chosen in the attached figure.