Step-by-step explanation:How do we set about finding the points in which two graphs y = f(x) and y = g(x) intersect?
We already know how to find where the graph of f(x) cuts the x−axis. That’s where y = 0. We calculate it by solving the equation f(x) = 0 .
When the graphs of y = f(x) and y = g(x) intersect , both graphs have exactly the same x and y values. So we can find the point or points of intersection by solving the equation f(x) = g(x). The solution of this equation will give us the x value(s) of the point(s) of intersection. We can then find the y value by putting the value for x that we have found into one of the original equations. That is by calculating either f(x) or g(x).
Example 1
Calculate the point of intersection of the two lines f(x) = 2x − 1 and g(x) = x + 1. First let’s look at a graph of the two functions. We can see the point of intersection is (2, 3).
