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Chapter 4: Problem 59

Graph \(f\) and \(g\) in the same rectangular coordinate system. Then find the point of intersection of the two graphs. Graph \(y=2^{x}\) and \(x=2^{y}\) in the same rectangular coordinate system.

Short Answer

Expert verified
After graphing the functions and finding the intersection, the intersection point was found to be (2,2). That is where the plots of \(y=2^{x}\) and \(x=2^{y}\) cross each other.

Step by step solution

01

Graphing the first function

The equation is \(y=2^{x}\). This is a basic exponential function. The graph starts from the point (0,1), since any number raised to 0 is 1. As x gets larger, y also gets larger. Start plotting this graph in the coordinate system.
02

Graphing the second function

The equation is \(x=2^{y}\). This is not a common form of a function but it still can be graphed. It is helpful to think of it as \(y=\log_{2}{x}\). The graph starts from the point (1,0), and as x gets larger, y also gets gradually larger. Plot this graph on the same coordinate system.
03

Find the point(s) of intersection

The intersection points are where the graphs of \(y=2^{x}\) and \(x=2^{y}\) cross each other. Inspect the drawn graphs and determine the specific points where the two curves intercept.

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