Part
A- Explain why the x-coordinates of the points where the graphs of the
equations y=2^-x and y=8^x+4 intersect are the solutions of the equation
2^-x=8^x+4
Because the intersection point has the a unique pair of (x,y) coordinates; such coordinates x,y belong to both equations.
Part B- Make tables to find the solution to 2^-x = 8^x+4. Take the integer values of x between -3 and 3.
x 2^ (-x) 8^(x + 4) <------ this is how I understand the right side
- 3 2^3 = 8 8^(1) = 8
- 2 2^2 = 4 8^(2) = 64
- 1 2^1 = 2 8^(3) = 512
0 2^0 = 1 8^(4) = 4,096
=> solution x = - 3
You can continue filling the table for x =1, x = 2 and x = 3, but the solution is already stated x = - 3.
Part C- How can you solve the equation 2^-x=8^x+4 graphically?
Draw the graphs of both equation is the same coordinate system and the solution will be the point where the two curves intersect each other.
