We define the floor function x to be the greatest integer not exceeding x. For e

Question

We define the floor function x to be the greatest integer not exceeding x. For example, [4] = 4, [[2.37]] = 2, [[-1]] =-1, [[-1.2]] =-2. Sketch by hand the graph of y = [x] by first tabulating the values of x for several numbers x. Then compare your graph with the plot form the grapher. What are the discontinuities of f(x) = [x] where the domain of x is -2.3 leq x leq 1.5? Are these removable discontinuities? At the numbers x where f(x) is not continuous, is f(x) continuous from the right? Is f(x) continuous from the left? (a) Use the Intermediate Value Theorem to show that if part of the graph of a polynomial function y = p(x) is located below the X-axis and above the X-axis, then it must intersect the X-axis at some number x = c. (This number c such that f(c) = 0 is called a zero of f(x)). In algebraic terms: if for some numbers a,b, a

Explanation / Answer

1)

f(x) is discontinous at all integers i.e., {-2,-1,0,1}

It is right continuousat those points as f(1.0001) = f(1)=1 and likewise

It's not removable discontinuity as f(x+) != f(x-) but it is Jump discontinuity

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