Question

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

According to the degree of freedom, if there are two unknowns to be determined, there should be two equations that are independent. In this case, the two equations y = 4^x and y = 2^x + 2. We equate the two equations to get x and y. x is equal to 1 and y is equal to 4. To solve the equation graphically, we plot the two graphs and see the point of intersection.