Question

Which of the following describes the graph of y=[x-2]?

O The graph has closed circles on the left of each step and open circles on the right and includes the step
y=-4 for-2≤ x < -1.
The graph has closed circles on the left of each step and open circles on the right and includes the step
y=-3 for-2 The graph has open circles on the left of each step and closed circles on the right and includes the step
y=-4 for-2 ≤ x < -1.
The graph has open circles on the left of each step and closed circles on the right and includes the step
y=-3 for-2

Answer 1

(a) The graph has closed circles on the left of each step and open circles on the right and includes the step y=-4 for-2 ≤ x < -1.

Explanation:

The floor function returns the greatest integer not exceeding the argument value. For a unit interval [n, n+1), where n is an integer, the value of the function is n.

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evaluation

For any x in the interval [-2, -1) the value of ...

y = ⌊x-2⌋

will be ...

y = ⌊-2 -2⌋ = -2 -2 = -4.

This will be the value of y for the entire interval [-2, -1).

The closed circle is on the left end of the step. For this function y=-4 is the first step.