Final answer:
To find f(1) for the function f(x) = 2x+1, we substitute x with 1, resulting in f(1) = 3. The graph of this function is a straight line with a positive slope that increases as x increases. For a continuous probability function, the function is a horizontal line and the probability is determined by the area under the curve.
Step-by-step explanation:
If we have the function f(x) = 2x+1, and we want to find the value of this function when we substitute in a 1, we can do this by replacing every x in the function with a 1.
The resulting calculation would be f(1) = 2(1) + 1, which simplifies to f(1) = 3.
The function is essentially an instruction to double the number you put in for x, and then add one to that result.
When visualizing the function f(x) for values of x from 0 to 20, the graph of the function would be a straight line with a constant slope, increasing as x increases. In a probability function that is continuous and equal to a constant within a range, such as f(x) = 12 for 0 ≤ x ≤ 12, the probability P (0 < x < 12) would be equal to 1, assuming the function is normalized over that range.
A function like f(x) = 20 for a range of x indicates a horizontal line at y = 20. If we're discussing the probability in terms of areas under the curve between specific values of x, the area would correspond to the probability of x falling within that range.