Question 1038928
selection B.


here's why:


start with x^2 <= 2x


subtract 2x from both sides of the equation to get x^2 -2x <= 0


solve for x^2 - 2x = 0 to get x = 0 or x = 2.


analyze the function when x < 0 and when x > 2 and when x between 0 and 2.


you will find that the function is positive when x < 0 and when x > 2 and that the function is negative when x is between 0 and 2.


therefore x have to be greater than or equal to 0 and less than or equal to 2.


in interval notation, that would be [0,2].


you can graph the function of x^2 - 2x = y and you will see that the graph is positive when x < 0 and that the graph is positive when x > 2 and that the graph is less than or equal to 0 when x is greater than or equal to 0 and less than or equal to 2.


here's the graph.


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