Maths Help Urgent Please
jhayes Sketch by hand the graph of a function that satisfies: (a) and (b). Is the function continuous at ? Explain.
Sketch by hand the graph of a function that satisfies: (a) and (b) and(c) . Is the function continuous from the left at ? Is the function continuous at from the right? Is the function continuous at ? Explain.
Sketch by hand the graph of a function that satisfies: (a) is not defined, (b) does not exist and (c) . Is the function continuous from the left at ? Is the function continuous at from the right? Is the function continuous at ? Explain.
4 (a) Use the Intermediate Value Theorem to show that if part of the graph of a polynomial function is located below the -axis and above the -axis, then it must intersect the -axis at some number . (This number such that is called a zero of ). In algebraic terms: if for some numbers , , but , then for some in the interval , . (b) Then give an example of a polynomial without a zero (a zero is a number such that ).
(c) Give an example of a function whose graph is above the -axis and below the -axis, yet does not intersect the -axis.