Question

Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 2−x and y = 8x+4 intersect are the solutions of the equation 2−x = 8x+4. (4 points)

Part B: Make tables to find the solution to 2−x = 8x+4. Take the integer values of x between −3 and 3. (4 points)

Part C: How can you solve the equation 2−x = 8x+4 graphically? (2 points)
PLEASE HELP

Answer 1

Part A:

The values of x and y are the same at the intersection. This means we can equate the y values to get the equations form for just x.

Part B:

x 2^-x 8^x+4

-3 8 8

-2 4 64

-1 2 512

0 1 4096

1 2 32,768

2 .25 262,144

3 .125 2097,152

-3 is the answer.

Part C:

You will plot the two functions on the correct coordinates, and then identify the point of intersection.

On the graph they should intersect at (-3,8)