Question

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

Answer 1

Answer:

Shown below

Step-by-step 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.