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Let's analyze the three given graphs with respect to the properties mentioned: domain, range (imagen), zeros (ceroes), y-intercept (ordenada), increasing intervals (C+), decreasing intervals (C-), and extrema (extremos).

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### a) Graph (a):
- **Domain (Dominio):** The graph covers all real numbers \( x \in (-\infty, \infty) \).
- **Range (Imagen):** The range is \( y \in (-\infty, 9] \), since the graph reaches a maximum value of 9.
- **Zeros (Ceros):** The graph crosses the x-axis at \( x = -5 \) and \( x = 1 \).
- **Y-intercept (Ordenada):** The y-intercept is \( y = 7 \) (the graph crosses the y-axis at this point).
- **Increasing intervals (C+):** The function is increasing for \( x \in (1, \infty) \).
- **Decreasing intervals (C-):** The function is decreasing for \( x \in (-\infty, -5) \) and \( x \in (-5, 1) \).
- **Extrema (Extremos):** There is a local maximum at \( x = -5 \) with \( y = 9 \).

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### b) Graph (b):
- **Domain (Dominio):** The domain is all real numbers \( x \in (-\infty, \infty) \).
- **Range (Imagen):** The range is \( y \in (-\infty, 7] \), since the maximum value of the graph is 7.
- **Zeros (Ceros):** The graph crosses the x-axis at \( x = -2 \) and \( x = 2 \).
- **Y-intercept (Ordenada):** The y-intercept is \( y = 3 \).
- **Increasing intervals (C+):** The function is increasing for \( x \in (-2, 0) \).
- **Decreasing intervals (C-):** The function is decreasing for \( x \in (0, 2) \) and \( x \in (2, \infty) \).
- **Extrema (Extremos):** There is a local maximum at \( x = -2 \) with \( y = 7 \) and no minimum.

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### c) Graph (c):
- **Domain (Dominio):** The graph is defined for \( x \in [-3, 9] \).
- **Range (Imagen):** The range is \( y \in [-5, 6] \).
- **Zeros (Ceros):** The graph crosses the x-axis at \( x = -2 \), \( x = 4 \), and \( x = 8 \).
- **Y-intercept (Ordenada):** The y-intercept is \( y = 0 \) (the graph passes through the origin).
- **Increasing intervals (C+):** The function is increasing for \( x \in (4, 9) \).
- **Decreasing intervals (C-):** The function is decreasing for \( x \in (-3, -2) \), and also in \( x \in (0, 4) \).
- **Extrema (Extremos):** There is a local minimum at \( x = 0 \) with \( y = -5 \) and a local maximum at \( x = 4 \) with \( y = 6 \).

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Would you like any further details or explanations about any part of this analysis?

Here are five related questions:
1. How do we find the domain of a function graphically?
2. What does it mean when a function has multiple zero points?
3. How do we identify local maxima and minima visually?
4. What is the relationship between the range and the y-values on a graph?
5. How can you determine whether a function is increasing or decreasing based on its slope?

**Tip:** When analyzing a graph, always pay attention to the behavior as \( x \to \infty \) and \( x \to -\infty \) to understand long-term trends.

Analyze the following graphs (Domain, range, zeros, y-intercept, C+, C-, growth, extrema).

Analyze graphs to determine the domain, range, zeros, y-intercepts, increasing and decreasing intervals, and extrema. This example covers important graph analysis concepts suitable for students in Grades 9-12.

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