Final answer:
To evaluate the function f(x)=3x+1, one substitutes the value of x into the equation. However, provided choices y=13x and y=x² do not match the decreasing positive slope characteristic described.
Step-by-step explanation:
The question pertains to the evaluation of the function f(x) at specific values or intervals and the understanding of its characteristics. The function given is f(x)=3x+1. To find the value of this function for a particular x, you simply substitute the value of x into the equation and solve.
For instance, at x=3, the function f(x) can be evaluated as follows:
f(3) = 3(3) + 1 = 9 + 1 = 10
This value is indeed positive, as mentioned in the first part of the question, which stated that f(x) has a positive value at x=3.
Next, considering a function with a positive slope that is decreasing in magnitude, we must identify a function whose rate of increase (slope) diminishes as x gets larger. Option a, y=13x, is a linear function with a constant slope and thus cannot be decreasing in magnitude. Option b, y=x², is a quadratic function whose slope increases with x if x is positive. Therefore, neither option a nor option b matches the described characteristics of f(x).
Lastly, when considering continuous probability functions like f(x) and restrictions such as 1 ≤ x ≤ 4 or 0 ≤ x ≤ 20, we address the behavior of the function within those intervals. For continuous probability functions, P(x > 3) would correspond to the area under the curve of f(x) for x values greater than 3 up to the upper limit of the interval, if defined.