The graph of p(x) = 4 * (0.75)^x - 3 starts at (0, 1), exhibits exponential decay, and approaches the line y = -3 as x increases.
The given exponential function is p(x) = 4 * (0.75)^x - 3. To graph this function, we can observe its key features. The base of the exponential term is 0.75, which is between 0 and 1, indicating decay. The multiplication by 4 scales the function vertically, and the subtraction of 3 shifts it downward.
Starting with the initial point when x = 0, p(0) = 4 * (0.75)^0 - 3 = 4 - 3 = 1. This gives us the point (0, 1) on the graph.
As x increases, the exponential term decreases, leading to a decrease in p(x). The graph will approach, but never touch, the horizontal line y = -3 due to the subtraction of 3 in the function.
To graph, plot additional points by selecting various x values and calculating p(x). As x becomes more negative, p(x) approaches zero, resulting in an asymptote at y = -3.
In summary, the graph of the exponential function p(x) = 4 * (0.75)^x - 3 starts at (0, 1), decays exponentially as x increases, and approaches the horizontal line y = -3.