We define the floor function to be the greatest integer not exceeding x. For example, Sketch by hand the graph of y by first tabulating the values of for several numbers x. Then compare your graph with the plot form the grapher. What are the discontinuities of f(x) = where the domain of x is -2.3 x 1.5? Are these removable discontinuities? As the numbers x where f(x) ix not continuous, is f(x) continuous from the right? IN /(X) continuous from the left? (a) Use the Intermediate Value Theorem to show r that if part of the graph of a polynomial function f p(x) is located below the x-axis and above the x-axis, then it must intersect the .Y-axis at some number x c. (This number c such that f(e) 0 is called a ztto of f(i)). In algebraic the: if foe some numbers a,b.a 0. then for some x in the interval (a,b), p(r) 0. (b) Then give an example of a polynomial p(x) without a zero (a zero in a number c such that p(c) - 0 ). Give an example of a function f(x) whose graph is above the X-axis and below the .Y-axis, vet f(x) does not intersect the x-axis. is the function f(x) continuous from the right at x 0? What is the domain of continuity of f(x)? Use the grapher for small x to verify what your conclusion,
