Final answer:
The domain of the exponential function is all real numbers. If assuming f(x) = 12% is an exponential function such as f(x) = Ce^{-12x}, the x-axis labels the variable x, and the y-axis labels the function f(x), with the decay rate at 12. P(x < 0.40) would be represented by shading the area under the curve from x = 0 to x = 0.40, but this doesn't apply to a constant probability function which would be a horizontal line.
Step-by-step explanation:
The question pertains to the characteristics of an exponential function and its graph. The domain of a continuous exponential function like f(x) = 12% is all real numbers, meaning it extends from negative infinity to positive infinity. This is because an exponential function can take any real number as an input.
When drawing the appropriate exponential graph, the x-axis will represent the variable x, and the y-axis will represent the function f(x). Since the function is described as f(x) = 12%, this implies a constant function rather than a traditional exponential function, which might be a typo. However, if we assume a typical exponential decay function such as f(x) = Ce^{-12x}, the decay rate would be 12, and you would see the graph decline rapidly as x increases. Assuming the presence of a typo and interpreting f(x) = 12% as a value that actually changes with x, the mean would depend on the specifics of the function.
If we need to show the probability P(x < 0.40) on the graph and assume an exponential distribution, we would be shading the area under the curve from x = 0 to x = 0.40. However, since f(x) = 12% suggests a probability of 12% which is constant, this does not typically apply, and such a graph would not be exponential. Instead, this would resemble a horizontal line at the y-value of 12% on a probability scale of 0 to 1.