Question

Please help! I’ll really appreciate it!

Answer 1

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.