7. Which of the following scenarios could be described by the real valued function f(x) = x3 + 3x2 + 2x?: *
A. A shoebox has a length that is 1 inch longer than its width and a height that is 1 inch longer than its length.
B. We want to know the product of three consecutive numbers
C. Start with a number. Cube it. Then square it and triple it. Then add twice the number.
D. A and B are correct.
E. A, B, and C are correct
(E) but C is ambiguous and unclear.
A&B for sure, but you'd better get C cleared up.
I will try and get C cleared up and maybe think of something else to put in place of it.
To determine which scenario is described by the function f(x) = x^3 + 3x^2 + 2x, we need to analyze the equation and compare it to the descriptions in each scenario.
Let's break down the equation:
f(x) = x^3 + 3x^2 + 2x
We can see that this function involves x being raised to different powers and then multiplied by different coefficients.
Now, let's analyze the scenarios:
A. A shoebox has a length that is 1 inch longer than its width and a height that is 1 inch longer than its length.
This scenario does not directly relate to the function f(x) = x^3 + 3x^2 + 2x. The equation does not mention anything about length, width, or height.
B. We want to know the product of three consecutive numbers.
This scenario also does not match the function f(x) = x^3 + 3x^2 + 2x. The equation involves a cubic term (x^3), which is not present in the scenario.
C. Start with a number. Cube it. Then square it and triple it. Then add twice the number.
This scenario matches the function f(x) = x^3 + 3x^2 + 2x. The equation describes the process of starting with a number (x), cubing it (x^3), squaring it (3x^2), tripling it (3x^2), and finally adding twice the original number (2x). Thus, this scenario aligns with the equation.
D. A and B are correct.
This option is incorrect because scenario B does not match the function f(x) = x^3 + 3x^2 + 2x.
E. A, B, and C are correct.
This option is also incorrect because scenario B does not match the function f(x) = x^3 + 3x^2 + 2x.
Therefore, the correct answer is C. Start with a number. Cube it. Then square it and triple it. Then add twice the number.