Question

98 POINTS AND BRAINLIEST TO BEST ANSWER!!!!!!!!!!!
Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 4^x and y = 2^x−2 intersect are the solutions of the equation 4^x = 2^x−2. (4 points)

Part B: Make tables to find the solution to 4^x = 2^x−2. Take the integer values of x between −3 and 3. (4 points)

Part C: How can you solve the equation 4^x = 2^x−2 graphically? (2 points)

Answer 1

Part A: the x-cordinates of where the graphs of the equations intercept are solutions because they make each side of the equation equal to the same value, making them equal. Basically, both functions put out the same value at that point x, making them equal.

Part B: See the attached image. From the tables we can see that both equations have the same output at x=-2, so that is where the graphs would intersect and that would be the solution. They both put out .0625 at x=-2

Part C: You can solve the equation 4^x=2^(x-2) graphically by plotting both sides of the equation as separate functions. In your graphing calculator, you would plot y=4^x and y=2^(x-2), and see at what x-value they intersect to find the solution