Question

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

Answer 1

Answer:

Shown below

Step-by-step explanation:

This function represents greatest integer function, which is the most famous of the step functions, which is denoted by $[x]$. So, this function is defined as:

$f(x)=[x] \ the \ greatest \ integer \ less \ than \ or \ equal \ to \ x.$. The graph of the greatest integer function has the following characteristics:

a) The domain of the function is the set of all real numbers.

b) The range of the function is the set of all integers.

c) The graph has a $y-intercept$ at $(0,0)$ and $x-intercept$ in the interval $[0,1)$

d) The graph is constant between each pair of consecutive integers.

e) The graph jumps vertically one unit at each integer value.

$f(x)=[x]-3$ tells us that the original function has been shifted 3 units downward. So the correct option has been marked in the square red below.