Question

Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 4ˣ and y = 2⁽ˣ⁻¹⁾ intersect are the solutions of the equation 4ˣ = 2⁽ˣ⁻¹⁾. (4 points)

Part B: Make tables to find the solution to 4ˣ = 2⁽ˣ⁻¹⁾. Take the integer values of x between −4 and 4. (4 points)

Part C: How can you solve the equation 4ˣ = 2⁽ˣ⁻¹⁾ graphically? (2 points)

Answer 1

The x-coordinates of the points where the graphs of the equations y = 4ˣ and y = 2⁽ˣ⁻¹⁾ intersect can be found by solving the equation 4ˣ = 2⁽ˣ⁻¹⁾. This can be done using tables or by graphically plotting the equations.

Step-by-step explanation:

In order to find the x-coordinates of the points where the graphs of the equations y = 4ˣ and y = 2⁽ˣ⁻¹⁾ intersect, we need to solve the equation 4ˣ = 2⁽ˣ⁻¹⁾.

To do this, we can make tables to find the solution. We take integer values of x between -4 and 4 and substitute them into both equations to see when they are equal.

Graphically, we can plot the two equations on a graph and find the x-coordinates where they intersect.