Determine if each function is continuous at the given value of a. Justify your answers using limits and the definition of continuity. If any functions are NOT continuous at a, determine which properties of continuity are satisfied and which properties fail. (a) f(x) = x² - 4x +3/x-3 at a = 3
(b) g(x) = x² - 4x + 3 - 3 if r73 if r = 3 at a=3.
(c) For the function g(x) in part (c), how would you "remove the discontinuity"? In other words, how could you re-define g(x) in order to make it continuous at a = 3? Be sure to write your new function g(x).

Were is the diagram?

First locate the turning point (vertex) of the graph. which is at the coordinates x=5 and y=9 or (5; 9).to determine whether it's a maximum or mininum value, you have to discern whether the vertex's y-value is the highest value or lowest value the graph can reach. since the vertex's y-value, 9 is the highest value the graph can reach, it will be a maximum.another basic way to determine whether the vertex's value is max or min is to see if the graph is smiling or sad. if it's smiling, the turning point/vertex would be a minimum, while a sad parabola would have a maximum y-value at the vertex.