https://file.aiquickdraw.com/mathbot/file/17265198786804rvcnx12.jpg

The given image shows a graph representing \( A(t) \), which models Cassio's altitude relative to the ground over time \( t \) (in minutes). The task is to match certain characteristics of the graph to corresponding statements.

### Let’s analyze the graph step-by-step:

1. **Máximo ou mínimo relativo (Maximum or minimum relative)**:
   - The graph shows a minimum at \( t = 6.5 \), where the altitude reaches the lowest point, approximately \(-12\) meters. 
   - This matches the statement: **"A menor altitude de Cássio foi de 12 metros abaixo do solo."**

2. **Intervalo positivo ou negativo (Positive or negative interval)**:
   - The graph is above the horizontal axis (altitude is positive) between \( t = 0 \) and \( t = 5 \), and it is below the horizontal axis (altitude is negative) between \( t = 5 \) and \( t = 8 \).
   - This matches the statement: **"Entre as marcas de 5 e 8 minutos, o elevador estava descendo."**

3. **Intervalo crescente ou decrescente (Increasing or decreasing interval)**:
   - The graph shows a decreasing interval between \( t = 3 \) and \( t = 6.5 \) and then an increasing interval from \( t = 6.5 \) to \( t = 10 \).
   - This matches the statement: **"Entre as marcas de 6,5 e 10 minutos, Cássio estava em subida."**

### Final Correspondence:

1. **Máximo ou mínimo relativo**: "A menor altitude de Cássio foi de 12 metros abaixo do solo."
2. **Intervalo positivo ou negativo**: "Entre as marcas de 5 e 8 minutos, o elevador estava descendo."
3. **Intervalo crescente ou decrescente**: "Entre as marcas de 6,5 e 10 minutos, Cássio estava em subida."

Would you like more details or have any other questions?

Here are 5 related questions you can explore:
1. What is the maximum altitude reached by Cassio?
2. How would the graph look if Cassio’s elevator stayed constant at a certain altitude?
3. What would happen if the graph represented Cassio descending continuously?
4. How do you identify the critical points of the function \( A(t) \) visually from the graph?
5. What are the time intervals where the elevator's motion changes direction?

**Tip**: When interpreting graphs, always look for key points such as intercepts, maxima, and minima to understand the underlying changes in the scenario.

The graph models Cassio's altitude over time. The task is to match certain graph characteristics (maximum/minimum relative, positive/negative interval, increasing/decreasing interval) with the corresponding statements about Cassio's altitude.

Learn how to analyze Cassio's altitude over time with a graph, identifying key intervals, maximum and minimum points. This exercise includes interpreting positive/negative intervals and increasing/decreasing trends. Suitable for students in Grades 9-10.

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