Let f and g be functions and suppose that the graphs of f and g intersect at the point (a,b). Since (a,b) is on the graph of f, b = f(a). (All points on the graph of f are of the form (x,f(x)).) But (a,b) is also on the graph of g, so b = g(a). Therefore, f(a) = g(a); i.e., a is a solution for the equation f(x) = g(x). Example 3. When they’re used well, graphs can help us intuitively grasp complex data. But as visual software has enabled more usage of graphs throughout all media, it has also made them easier to use in a careless or dishonest way — and as it turns out, there are plenty of ways graphs can mislead and outright manipulate. Lea Gaslowitz shares some things to look out for.