Is the floor function increasing or decreasing or both in the interval [0,1)I was attempting a quiz in which I encountered this question, Now the graph of the floor function is constant in the interval [0,1) so technically the function should be neither increasing nor decreasing, but the answer to the question is its both increasing and decreasing. So is the answer wrong or am I unaware of a concept?Similarly, there was another question about the function f ( x ) = x 2 − 3 x + 2 in the interval [ 0 , i n f ] but the graph of the function comes down from 0 and there is a critical point at 1 and then goes up, so is decreasing and increasing in the interval [ 0 , i n f ) but the answer is its neither increasing nor decreasing, now one of my classmates gave me a line of reasoning that f ′ ( x ) &lt;= 0 a n d f ′ ( x ) &gt;= 0 in the inerval [ 0 , i n f ) which implies f ′ ( x ) = 0 but I'm not really convinced with the argument because the graph clearly shows that the function is decreasing then increasing. So am I missing a concept here or the answers are wrong?

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Is the floor function increasing or decreasing or both in the interval [0,1)I was attempting a quiz in which I encountered this question, Now the graph of the floor function is constant in the interval [0,1) so technically the function should be neither increasing nor decreasing, but the answer to the question is its both increasing and decreasing. So is the answer wrong or am I unaware of a concept?Similarly, there was another question about the function   f  (  x  )  =      x    2    −  3  x  +  2 in the interval   [  0  ,  i  n  f  ] but the graph of the function comes down from 0 and there is a critical point at 1 and then goes up, so is decreasing and increasing in the interval   [  0  ,  i  n  f  ) but the answer is its neither increasing nor decreasing, now one of my classmates gave me a line of reasoning that       f    ′    (  x  )  &amp;lt;=  0  a  n  d      f    ′    (  x  )  &amp;gt;=  0 in the inerval   [  0  ,  i  n  f  ) which implies       f    ′    (  x  )  =  0 but I&#039;m not really convinced with the argument because the graph clearly shows that the function is decreasing then increasing. So am I missing a concept here or the answers are wrong?

Arjun Wright · Accepted Answer

Step 1increasing function:   x  &amp;gt;  y     ⟹     f  (  x  )  ≥  f  (  y  )decreasing function:   x  &amp;gt;  y     ⟹     f  (  x  )  ≤  f  (  y  )strictly increasing function:   x  &amp;gt;  y     ⟹     f  (  x  )  &amp;gt;  f  (  y  )strictly decreasing function:   x  &amp;gt;  y     ⟹     f  (  x  )  &amp;lt;  f  (  y  )Step 2A constant function is increasing and decreasing. But it is neither strictly increasing nor strictly decreasing.For   f  (  x  )  =      x    2    −  3  x  +  2, it is increasing on   [  1.5  ,  ∞  ) and decreasing on [0,1.5]. But it is neither increasing nor decreasing on   [  0  ,  ∞  ).

Is the floor function increasing or decreasing or both in the interval [0,1)

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