High School

This function is:

\[ Q_H = 60000 - 40P_H + 20P_C + 5H + 0.1I_H + 0.0001A_H \]

1. Characterize this function by selecting all applicable options from the following list:

- Univariate
- Bivariate
- Multivariate
- Linear
- Exponential
- Logarithmic
- Curvilinear
- 1st Degree
- 2nd Degree
- 3rd Degree
- Additive
- Multiplicative
- Linearly Homogeneous

Answer :

Let's analyze the given function:

[tex]Q_H = 60000 - 40P_H + 20P_C + 5H + 0.1I_H + 0.0001A_H[/tex]

Characterization of the Function:

  1. Multivariate:

    • The function has more than one independent variable ([tex]P_H, P_C, H, I_H, A_H[/tex]), so it is not univariate or bivariate, but multivariate.

  2. Linear:

    • The function is linear because all the variables ([tex]P_H, P_C, H, I_H, A_H[/tex]) are raised to the power of 1.

  3. 1st Degree:

    • The highest power of any variable is 1, meaning it's a first-degree function.

  4. Additive:

    • The function combines terms with addition or subtraction, thus it is considered additive.

  5. Not Exponential, Logarithmic, Curvilinear, or Multiplicative:

    • The function does not feature exponential growth, logarithmic characteristics, curvilinear shapes, or multiplicative relationships between variables.

  6. Not Linearly Homogeneous:

    • A linearly homogeneous function, if multiplied by a scalar, increases each variable by that scalar. Here, that property isn't applicable because the constant 60000 won’t scale proportionally with all the variables in such a way.

Summary:

  • Multivariate
  • Linear
  • 1st Degree
  • Additive

This type of analysis is fundamental in college-level mathematics, especially in courses involving linear algebra or econometrics, where understanding the nature of functions is essential in modeling real-world scenarios. If you have further questions or need more examples, feel free to ask!

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