MATH SOLVE

5 months ago

Q:
# The function y = [x] is defined as follows: for any input x, the output is the smallest integer that is greater than or equal to x (“rounding up” any non-integer to the next integer).Draw the graph of y = [x] for -2 ≤ x ≤ 2. Upload a handwritten copy of your graph as your final answer.

Accepted Solution

A:

For the integer values of the interval -2 ≤ x ≤ 2, that is for {-2, -1, 0, 1, 2}, the function works as follows:

[-2]=-2, [-1]=-1 [0]=0 [1]=1 [2]=2,

as each of -2, -1, 0, 1, 2 is smaller or equal to themselves.

Each value in between, produces the integer to their right.

For example, [1,25]=2, because 2 is the smallest integer, greater than 1,25.

Thus, the output of each non-integer value is the closest integer to the right. Some more examples:

[0,7]=1, [0.46]=1, [-0,5]=0, [-1,33]=-1.

The graph is as shown in the picture.

[-2]=-2, [-1]=-1 [0]=0 [1]=1 [2]=2,

as each of -2, -1, 0, 1, 2 is smaller or equal to themselves.

Each value in between, produces the integer to their right.

For example, [1,25]=2, because 2 is the smallest integer, greater than 1,25.

Thus, the output of each non-integer value is the closest integer to the right. Some more examples:

[0,7]=1, [0.46]=1, [-0,5]=0, [-1,33]=-1.

The graph is as shown in the picture.