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Which graph represents the function on the interval [−3, 3]?

f(x)=⌊x⌋−3

 

Options:

Graph of a step function. The horizontal axis ranges from negative 4 to 4 in increments of 1. The vertical axis ranges from negative 7 to 3 in increments of 1. The function consists of 6 line segments, each with an open endpoint to the left, a closed endpoint to the right and a length of 1 unit. First segment has endpoints begin ordered pair negative 3 comma negative 5 end ordered pair and begin ordered pair negative 2 comma negative 5 end ordered pair. Second segment has endpoints begin ordered pair negative 2 comma negative 4 end ordered pair and begin ordered pair negative 1 comma negative 4 end ordered pair. Third segment has endpoints begin ordered pair negative 1 comma negative 3 end ordered pair and begin ordered pair 0 comma negative 3 end ordered pair. This pattern continues. The point begin ordered pair negative 3 comma negative 6 end ordered pair is plotted.

Graph of a step function. The horizontal axis ranges from negative 4 to 4 in increments of 1. The vertical axis ranges from negative 7 to 3 in increments of 1. The function consists of 6 line segments, each with an open endpoint to the left, a closed endpoint to the right and a length of 1 unit. First segment has endpoints begin ordered pair negative 3 comma negative 6 end ordered pair and begin ordered pair negative 2 comma negative 6 end ordered pair. Second segment has endpoints begin ordered pair negative 2 comma negative 5 end ordered pair and begin ordered pair negative 1 comma negative 5 end ordered pair. Third segment has endpoints begin ordered pair negative 1 comma negative 4 end ordered pair and begin ordered pair 0 comma negative 4 end ordered pair. This pattern continues.

Graph of a step function. The horizontal axis ranges from negative 4 to 4 in increments of 1. The vertical axis ranges from negative 7 to 3 in increments of 1. The function consists of 6 line segments, each with a closed endpoint to the left, an open endpoint to the right and a length of 1 unit. First segment has endpoints begin ordered pair negative 3 comma negative 5 end ordered pair and begin ordered pair negative 2 comma negative 5 end ordered pair. Second segment has endpoints begin ordered pair negative 2 comma negative 4 end ordered pair and begin ordered pair negative 1 comma negative 4 end ordered pair. Third segment has endpoints begin ordered pair negative 1 comma negative 3 end ordered pair and begin ordered pair 0 comma negative 3 end ordered pair. This pattern continues. The point begin ordered pair 3 comma 1 end ordered pair is plotted.

Graph of a step function. The horizontal axis ranges from negative 4 to 4 in increments of 1. The vertical axis ranges from negative 7 to 3 in increments of 1. The function consists of 6 line segments, each with a closed endpoint to the left, an open endpoint to the right and a length of 1 unit. First segment has endpoints begin ordered pair negative 3 comma negative 6 end ordered pair and begin ordered pair negative 2 comma negative 6 end ordered pair. Second segment has endpoints begin ordered pair negative 2 comma negative 5 end ordered pair and begin ordered pair negative 1 comma negative 5 end ordered pair. Third segment has endpoints begin ordered pair negative 1 comma negative 4 end ordered pair and begin ordered pair 0 comma negative 4 end ordered pair. This pattern continues. The point begin ordered pair 3 comma 0 end ordered pair is plotted.

Guest Mar 10, 2018
 #1
avatar+87333 
+1

This is a floor function graph

For any x, floor (x)  is defined as the greatest integer less than or equal to x

 

For  example, let x  = 3  ....so....

floor (3)  = 3

So

floor(3)  - 3  =  0

 

And   let x  = 2.5     .....so....

floor (2.5)  = 2 

So

floor (2.5) -  3  =  2  - 3  =  -1

 

The last graph is correct

 

cool cool cool

CPhill  Mar 10, 2018

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