which graph can be used to solve the equation 2^x - 1 = x + 2?

Explanation:

Step1: Rewrite the equation for graph - ing

To solve the equation (2^{x}-1=x + 2) graphically, we can consider two functions (y_1=2^{x}-1) and (y_2=x + 2). The solution of the equation (2^{x}-1=x + 2) is the (x) - value of the intersection point of the graphs of (y = 2^{x}-1) and (y=x + 2). The function (y = 2^{x}-1) is an exponential - type function. Its base is (a = 2>1), and when (x = 0), (y=2^{0}-1=0). It has a horizontal asymptote at (y=-1). The function (y=x + 2) is a linear function with a slope (m = 1) and a (y) - intercept (b = 2).

Step2: Analyze the intersection

We need to find the graph that shows the intersection of an exponential - type curve (y = 2^{x}-1) and a straight - line (y=x + 2). The exponential function (y = 2^{x}-1) is increasing for all real (x) values, and the linear function (y=x + 2) is also increasing.

Answer:

The graph that shows an increasing exponential - type curve (y = 2^{x}-1) and an increasing straight - line (y=x + 2) intersecting at a point. Without the actual labels on the given graphs, we know that we are looking for a graph with an exponential curve (starting from near (y=-1) for negative (x) values and increasing rapidly) and a straight - line with a slope of 1 and (y) - intercept of 2 intersecting each other.