R^2 at SCC In this lesson you will learn how to tell if a line on a graph represents a function by mapping inputs to outputs. Create your free account Teacher Student. For example, consider the function y = 2x + 1. We're asked: Do the points on the graph below represent a function? We can also represent functions using graphs by plotting all the ordered pairs of a function on a coordinate axis. So if we look here, they've graphed the point--it looks like negative 1, 3, so that's the point negative 1, 3. When a function is given as a graph, we have a nice test we can use to determine if the graph represents a function. You can represent your function by making it into a graph. The [math]cos(0) = 1 [/math]and [math]sin(0)=0[/math]. Simple. If an algebraic equation defines a function, then we can use the notation f (x) = y. vertical line test to determine if a graph represents a function which graphs are functions? Graphs come in all sorts of shapes and sizes. This test is called the vertical line test. THE VERTICAL LINE TEST A graph (or set of points) in the plane is a FUNCTION if no vertical line contains more than one of its points. In algebra, there are 3 basic types of graphs you'll see most often: linear, quadratic, and exponential. In a graph, we have what is called the vertical line test, in which if a vertical line crosses the graph in two or more points, then it is NOT a function. All points must lie along the curve for it to be a function. In a table, if a value is given in the x table twice with separate y values, then it is NOT a function. If any vertical line intersects the graph more than once, then the graph does not represent a function. Determine whether a graph is a function. Answer and Explanation: if you know what y equals, say y = 2x. We can easily determine whether or not an equation represents a function by performing the vertical line test on its graph. 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