https://file.aiquickdraw.com/mathbot/file/1725561847703xcezvs3x.jpg

I see that you've uploaded an image with a mathematical problem involving the planets in our Solar System, their mean distance from the Sun, and their orbital period. Let me help you analyze the problem.

The image presents the following:

1. **Planets Data**: A table showing the mean distance of each planet from the Sun (in Astronomical Units, AU) and their corresponding orbital period (in years). This data is for the eight major planets:
   - Mercury: 0.39 AU, 0.241 years
   - Venus: 0.72 AU, 0.615 years
   - Earth: 1.00 AU, 1.00 years
   - Mars: 1.52 AU, 1.88 years
   - Jupiter: 5.2 AU, 11.9 years
   - Saturn: 9.58 AU, 29.4 years
   - Uranus: 19.2 AU, 83.7 years
   - Neptune: 30.0 AU, 164.8 years

2. **Function Analysis**:
   The task is to define the domain and range of the function that describes the relationship between the mean distance and the orbital period.

**Domain**: The domain represents all possible values of the independent variable (mean distance from the Sun in AU). So the domain is the set of all mean distances in the table:
\[ D = \{0.39, 0.72, 1.00, 1.52, 5.2, 9.58, 19.2, 30.0\} \]

**Range**: The range represents the set of all possible values of the dependent variable (orbital period in years):
\[ R = \{0.241, 0.615, 1.00, 1.88, 11.9, 29.4, 83.7, 164.8\} \]

The rest of the image seems to include multiple-choice options to identify the domain, range, and the type of relationship (possibly testing for direct or inverse variation).

If you want further analysis or have specific questions about the next part of the problem, feel free to ask!

### Would you like more details or explanations on any part of this?
### Here are 5 related questions for further practice:
1. How would you determine whether the relationship between mean distance and orbital period is linear or exponential?
2. Can you find the approximate orbital period of a planet at 2 AU from the Sun?
3. How would the domain and range change if more planets or celestial bodies were added?
4. What is the significance of the Astronomical Unit (AU) in describing planetary orbits?
5. How does Kepler’s Third Law relate to this data?

### Tip:
Kepler’s Third Law can help you understand the relationship between the distance of planets from the Sun and their orbital periods—specifically, the square of the period is proportional to the cube of the distance from the Sun.

The table shows the orbital period of the eight major planets in our Solar System given their mean distance from the Sun. Define the domain and range of the function and state whether it is continuous, discrete, or neither.

Analyze the orbital period and mean distance of planets from the Sun. Define the domain and range of the function for the eight major planets: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune. Learn whether the function is continuous or discrete, and how Kepler's Third Law relates to planetary orbits.

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