Timothy W. answered • 07/08/19

Virginia Tech Graduate and Mathematics Minor with STEM Experience

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