How do coordinates represent solutions

Question

How are the coordinates (x,y) used to represent a solution to f(x)=g(x) for different types of functions (radical, rational, quadratic, linear). In other words, how is the ordered pair a solution to  if  and represent function types 

Answer 1

In a solution like this, the "x coordinate" denotes the value of x for which both functions output the same value, and the "y coordinate" denotes what that output value actually is.

Consider the following example:

f(x) = ¹/_(x+1)

g(x) = e^x

If we were to look for the intersection of these two functions, we would get the ordered pair (0,1). This informs us that both functions take the same value when evaluated at x = 0 (that is, f(0) = g(0), as desired) and that both functions take the value of 1 for that input (that is, f(0) = 1 and g(0) = 1).

The fact that the solution contains both coordinates reflects the fact that if we know the two functions have the same value for a given input value (x), then we necessarily know the output value of both functions for that input (because they must be the same).

I hope this helps!

Tim W