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Part A:
Explain why the x-coordinates of the points where the graphs of the equations y=4^-x and y= 8^-x-1 intersect are the solutions of the equation 4^-x = 8^-x-1.

Part B:
Make tables to find the solution to 4^-x= 8^-x-1. Take the integer values of x between -3 and 3.

Part C:
How can you solve the equation 4^-x = 8^-x-1 graphically?

Respuesta :

Part A. The graphs intersect at a point (x,y) which means that this point lies on both graphs. We already know how y is related to x for each graph. The left hand side of the equation is the y value for one graph and the right hand side the y value for the other. So the equation actually says y=y, the y value for both being the same at the point of intersection. Solving the equation for x will supply the common x coord.
Part B.
TABLE
x y₁ y₂ (y values for respective functions)
-3 64 64
-2 16 8
-1 4 1
0 1 1/8
1 1/4 1/64
2 1/16 1/512
3 1/64 1/4096
From the table x=-3 is a solution and y=64. Solution is (-3,64).
Part C
Plot the two graphs using the table as a guide. The graphs should intersect at (-3,64).

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