Ji! : )
part a: explain why the x-coordinates of the points where the graphs of the equations y = 2^x and y = 4^x−2 intersect are the solutions of the equation 2^x = 4^x−2. (4 points)
part b: make tables to find the solution to 2^x = 4^x−2. take the integer values of x between −4 and 4. (4 points)
part c: how can you solve the equation 2^x = 4^x−2 graphically? (2 points)

Part A

The x coordinates are the inputs of the functions f(x) = 2^x and g(x) = 4^(x-2)

If we have some input x that leads to f(x) = g(x), then this x value is a solution. It makes the equation f(x) = g(x) true. This is why the x coordinate of the intersection point of y = 2^x and y = 4^(x-2) is the solution.

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Part B

See attached for the table. See figure 1.

This is how you get the results you see in the table
Plug x = -4 into f(x) to get:
f(x) = 2^x
f(-4) = 2^(-4)
f(-4) = 0.0625

Do the same for g(x):
g(x) = 4^(x-2)
g(-4) = 4^(-4-2)
g(-4) = 4^(-6)
g(-4) = 0.000244140625

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Plug x = -3 into f(x) to get:
f(x) = 2^x
f(-3) = 2^(-3)
f(-3) = 0.125

Do the same for g(x):
g(x) = 4^(x-2)
g(-3) = 4^(-3-2)
g(-3) = 4^(-5)
g(-3) = 0.0009765625

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Plug x = -2 into f(x) to get:
f(x) = 2^x
f(-2) = 2^(-2)
f(-2) = 0.25

Do the same for g(x):
g(x) = 4^(x-2)
g(-2) = 4^(-2-2)
g(-2) = 4^(-4)
g(-2) = 0.00390625

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Plug x = -1 into f(x) to get:
f(x) = 2^x
f(-1) = 2^(-1)
f(-1) = 0.5

Do the same for g(x):
g(x) = 4^(x-2)
g(-1) = 4^(-1-2)
g(-1) = 4^(-3)
g(-1) = 0.015625

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Plug x = 0 into f(x) to get:
f(x) = 2^x
f(0) = 2^(0)
f(0) = 1

Do the same for g(x):
g(x) = 4^(x-2)
g(0) = 4^(0-2)
g(0) = 4^(-2)
g(0) = 0.0625

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Plug x = 1 into f(x) to get:
f(x) = 2^x
f(1) = 2^(1)
f(1) = 2

Do the same for g(x):
g(x) = 4^(x-2)
g(1) = 4^(1-2)
g(1) = 4^(-1)
g(1) = 0.25

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Plug x = 2 into f(x) to get:
f(x) = 2^x
f(2) = 2^(2)
f(2) = 4

Do the same for g(x):
g(x) = 4^(x-2)
g(2) = 4^(2-2)
g(2) = 4^(0)
g(2) = 1

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Plug x = 3 into f(x) to get:
f(x) = 2^x
f(3) = 2^(3)
f(3) = 8

Do the same for g(x):
g(x) = 4^(x-2)
g(3) = 4^(3-2)
g(3) = 4^(1)
g(3) = 4

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Plug x = 4 into f(x) to get:
f(x) = 2^x
f(4) = 2^(4)
f(4) = 16

Do the same for g(x):
g(x) = 4^(x-2)
g(4) = 4^(4-2)
g(4) = 4^(2)
g(4) = 16

Note that since the input x = 4 leads to the same output (16) this makes x = 4 a solution.

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Part C

To solve graphically, you need to use the table in part B to draw a curve through the set of points. Then determine where the curves cross (if they cross at all). You may need to adjust the graph window if the intersection point is off the screen.

See figure 2 for the graph (attached as well). Point A in green is the intersection point. 
A = (4,16) 
so x = 4 is the solution to f(x) = g(x).