Please help me solve each question!!!

What is the definition of continuity of a function f(x) at x = a? If the function f(x)= - continuous at x = 0? Explain. 2 For each of the following, write down a formula of a function other than those given in the book: a) A function f(x) with an infinite discontinuity f (x) = b) A function g(x) with a jump discontinuity g ( x) = c) A function h(x) with a removable discontinuity h (x) = 3 Which function families are continuous everywhere in their domains? 4 How do we know that the function g(x) = x' -3 has at least one root between x = 1 and x = 2? Use the Intermediate Value Theorem in your explanation. 5 BOTTOM LINE QUESTION Make the function h(x)= _ sin x a continuous function at x = 0. x