MATH 1108 Lecture Notes - Lecture 1: Counterexample

• School: Fordham University
• Department: Mathematics
• Course: MATH 1108
• Professor: Sixian Jin

Document Summary

Function: a function is a correspondence between two sets of elements such that to each element in the. Rst set, there corresponds one and only one element in the second set. Graph of a function: the collection of all paired points {(x, y)} on the xy-plane. Example: draw the graph of functions y = x + 1 and y = x2. y=x2 y=xtl. Vertical line test: if a vertical line can be drawn so that it intersects the graph at most one time, then this graph is the graph of a function. Function evaluation: we usually use the symbol f (x) in place of y to denote the function, with an emphasis of the variable x. Example: let f (x) = 5x 2 and g(x) = x2 2x: evaluate f (0) and g(0). O: if f (x) = f (x) + g(x),then evaluate f (1) 2: evaluate f (x + h) and g( 2x).