Answer:
Option 4
Step-by-step explanation:
The most famous of the step functions is the greatest integer function, which is denoted by [tex][x][/tex]. So, this function is defined as:
[tex]f(x)=[x] \ the \ greatest \ integer \ less \ than \ or \ equal \ to \ x.[/tex].
These are the characteristic of this function:
- The domain of the function is the set of all real numbers.
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The range of the function is the set of all integers.
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The graph has a [tex]y-intercept[/tex] at [tex](0,0)[/tex] and [tex]x-intercept[/tex] in the interval [tex][0,1)[/tex]
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The graph is constant between each pair of consecutive integers.
- The graph jumps vertically one unit at each integer value.
However, we have made some changes to the parent function by multiplying it by 3 and making a shift 4 units downward. Finally, we get the graph shown below that matches the fourth option.
