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 El costo de la boleta en un cinema depende de la edad de la persona, como lo muestra la tabla. Como sería la gráfica


The table you provided shows the cost of a cinema ticket depending on the age of the person. Here's the information extracted from the table:

- Age (in years, \(X\)) from 0 to 8: Cost (\(Y\)) = 5,000 pesos.
- Age more than 8 and up to 16: Cost (\(Y\)) = 7,000 pesos.
- Age more than 16 and up to 56: Cost (\(Y\)) = 10,000 pesos.
- Age more than 56: Cost (\(Y\)) = 6,000 pesos.

To graph this, we would create a piecewise function where each segment corresponds to the age ranges given in the table. On the X-axis, we would plot age, and on the Y-axis, we would plot the cost in pesos.

Here’s how the graph would be structured:

1. **X from 0 to 8:** Horizontal line at \( Y = 5000 \).
2. **X from 8 to 16:** Horizontal line at \( Y = 7000 \).
3. **X from 16 to 56:** Horizontal line at \( Y = 10000 \).
4. **X greater than 56:** Horizontal line at \( Y = 6000 \).

### Graph Description:
- The graph would be a series of horizontal lines (steps).
- The first line would be from \( X = 0 \) to \( X = 8 \) at \( Y = 5000 \).
- The second line would start at \( X = 8 \) and go to \( X = 16 \) at \( Y = 7000 \).
- The third line would start at \( X = 16 \) and go to \( X = 56 \) at \( Y = 10000 \).
- The final line would start at \( X = 56 \) and continue indefinitely at \( Y = 6000 \).

Would you like a visual representation of this graph, or do you have any specific questions about it?

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### Related Questions:
1. What is the mathematical function that represents this cost distribution?
2. How would the graph change if the costs were to increase by 10% for each category?
3. What would the equation look like if the age groups had overlapping intervals?
4. How could you express this cost distribution using a piecewise function notation?
5. What would happen to the graph if an additional age category, say 56 to 70, were added?
6. How does the piecewise nature of the graph reflect in real-world applications?
7. How could the graph help in optimizing ticket sales in a cinema?
8. What would be the total revenue if 100 tickets were sold in each age group?

### Tip:
When graphing piecewise functions, it’s crucial to clearly mark the endpoints of each interval to avoid confusion, especially when dealing with real-world data.

Explore how cinema ticket costs vary with age using a piecewise function graph. Learn about the cost structure for different age groups: 0-8 years, 8-16 years, 16-56 years, and over 56 years. Suitable for high school students studying piecewise functions and mathematical modeling.

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