college algebra about functions

Question

1. If the domain and range of a function consists of real numbers, then you can graph it by plotting all ordered pairs of the form (x, f(x)). How can you tell by looking at a graph if it represents a function?

Answer 1

The standard way to tell if a graph represents a function is the "Vertical Line Test" - if a vertical line drawn at every point along the x-axis intercepts the graph no more than once, then the graph represents a function. The reason it works is that every x in the domain of a function maps to one and only one value of y.