Algebra 1 Help Please

Question

Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 4^−x and y = 2^x + 3 intersect are the solutions of the equation 4^−x = 2^x + 3.

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

Part C: How can you solve the equation 4^−x = 2^x + 3 graphically?

Answer 1

Because they are both exponential function of x...

The intersection point of ANY two functions f(x) and g(x) can be

found by solving the equation f(x)=g(x)

However, you may NOT be able to solve the equation algebraically.

Instead, you will have to look at their graphs on the same plot and

ZOOM in to point at where they meet.

www.desmos.com has an excellent function plotter by the way...

Some people prefer to define the function H(x) = f(x)-g(x) and see

where that function is zero ( namely where it crosses the x-axis)

In this case, you would define f(x) = 4^(-x) = 1/(4^x) and g(x) = 2^x + 3.

Then you can graph those two functions and find where they meet.

Alternatively, you can define H(x) = f(x) - g(x) = 4^(-x) - 2^x - 3 = 1/(4^x) - 2^x - 3

Per desmos.com. the intersection is at x=-0.91