Look at where the graph crosses the X-axis at the point [math]x=0[/math]. At the line which crosses the x axis at 3, y will = 6. 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. if you know what y equals, say y = 2x. In this lesson you will learn how to tell if a line on a graph represents a function by mapping inputs to outputs. Graphs come in all sorts of shapes and sizes. We can easily determine whether or not an equation represents a function by performing the vertical line test on its graph. For example, consider the function y = 2x + 1. The [math]cos(0) = 1 [/math]and [math]sin(0)=0[/math]. Put x into the equation, say 3, so y = 2*3 = 6. 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. This test is called the vertical line test. When a function is given as a graph, we have a nice test we can use to determine if the graph represents a function. Simple. Instructional video. R^2 at SCC If an algebraic equation defines a function, then we can use the notation f (x) = y. So in order for the points to represent a function, for every input into our function, we can only get one value. If each x value has a unique y value, then the graph represents a function. So if we look here, they've graphed the point--it looks like negative 1, 3, so that's the point negative 1, 3. All points must lie along the curve for it to be a function. We're asked: Do the points on the graph below represent a function? which graphs are functions? Determine whether a graph is a function. vertical line test to determine if a graph represents a function If any vertical line intersects the graph more than once, then the graph does not represent a function. 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