Final answer:
To graph the function 2^x - 3, plot select points, and sketch the curve that passes through them. It has a horizontal asymptote at y = -3, grows exponentially as x increases, and does not have a rate of decay or defined mean. The request for shading an area related to probability is irrelevant for this function.
Step-by-step explanation:
The student has asked about drawing the graph of the exponential function 2x - 3 and discussing its properties.
To draw this graph, we start by plotting points for select values of x, and then sketch the curve that represents the function.
Some key properties to note:
The graph approaches y = -3 as x approaches negative infinity, which is the horizontal asymptote.
As x increases, the function rapidly grows towards positive infinity.
The rate of decay is not applicable here because this is an exponential growth function.
There is no defined mean for this function as it is not symmetrical or periodic.
To answer the second part of the question regarding shading the area to represent the probability that a student has less than $0.40 in his or her pocket would typically require us to be looking at a probability distribution function, which is not the case with 2x - 3.
Therefore, no shading for probability will be done for this particular function.