MthT 430 Notes Chapter 3b More about Functions

If f is a function, the set

{(x,f(x)) | x ∈ domain f }

is identified with the graph of f.

A function is one-to-one or bijective if f(x) = f(y) implies that x = y.

If f is a function, then a function g is an extension of f if

•

domain(f) ⊂ domain(g).

•

For all x ∈ domain(f), g(x) = f(x).

Definition. If f is a function, then a function g is an extension of f if

graph(f) ⊂ graph(g).

A set A of ordered pairs {(x,y)} is a function (graph of a function) if it passes the vertical line test: no vertical line intersects A in more than one point. If A is the graph of a function f, then the function is one-to-one if A passes the horizontal line test: no horizontal line intersects A in more than one point. Think about what the meaning of vertical/horizontal line .

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