Question

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

Answer 1

Answer: It was the third graph for me.

Step-by-step explanation: I took the test and that was the correct answer

Answer 2

Shown below

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.