https://file.aiquickdraw.com/mathbot/file/1728527132599u1nggb16.jpg

Let's analyze the graph step by step to answer the given questions:

### a. **Domain**  
The domain of a function refers to all the possible \( x \)-values the function can take. From the graph, the function continues indefinitely in both the left and right directions (the arrows on the graph confirm this). Therefore, the domain is:  
\[ \text{Domain: } (-\infty, \infty) \]

### b. **Range**  
The range refers to all possible \( y \)-values the function can achieve. From the graph, the function appears to cover all \( y \)-values from about \( -5 \) to infinity (since the function rises indefinitely). Therefore, the range is:  
\[ \text{Range: } [-5, \infty) \]

### c. **x-intercepts**  
The \( x \)-intercepts are the points where the function crosses the \( x \)-axis (where \( y = 0 \)). From the graph, the function crosses the \( x \)-axis at \( x = -2 \), \( x = 0 \), and \( x = 2 \). So, the \( x \)-intercepts are:  
\[ \text{x-intercepts: } (-2, 0), (0, 0), (2, 0) \]

### d. **y-intercepts**  
The \( y \)-intercept is the point where the function crosses the \( y \)-axis (where \( x = 0 \)). From the graph, the function crosses the \( y \)-axis at \( (0, 0) \). So, the \( y \)-intercept is:  
\[ \text{y-intercept: } (0, 0) \]

### e. **Local Maximums**  
A local maximum occurs where the function changes from increasing to decreasing. This happens around \( x = -1 \), where the graph reaches a peak. Therefore, the local maximum occurs at approximately:  
\[ \text{Local Maximum: } (-1, 1) \]

### f. **Local Minimums**  
A local minimum occurs where the function changes from decreasing to increasing. This occurs around \( x = 1 \), where the graph reaches a low point. So, the local minimum is approximately:  
\[ \text{Local Minimum: } (1, -2) \]

### g. **Where the function is increasing and decreasing**  
- **Increasing**: The function increases where the slope is positive. From the graph, the function is increasing on two intervals: from \( (-\infty, -1) \) and from \( (1, \infty) \).
- **Decreasing**: The function decreases where the slope is negative. This occurs between \( (-1, 1) \).

So, the intervals are:  
- Increasing: \( (-\infty, -1) \cup (1, \infty) \)  
- Decreasing: \( (-1, 1) \)

### h. **End Behavior**  
End behavior describes how the function behaves as \( x \) approaches positive and negative infinity.  
- As \( x \to \infty \), \( f(x) \to \infty \) (the function rises).  
- As \( x \to -\infty \), \( f(x) \to -\infty \) (the function falls).

Thus, the end behavior is:  
\[ \lim_{x \to \infty} f(x) = \infty \]  
\[ \lim_{x \to -\infty} f(x) = -\infty \]

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Would you like further details on any part of this explanation? Here are some related questions:

1. Can we explore in more detail how to find the intervals of increase and decrease?
2. How does the graph show concavity and points of inflection?
3. What other methods can be used to verify the local maximum and minimum?
4. How would you approach finding exact values for critical points?
5. How do we determine the symmetry of the function from the graph?

**Tip**: Always check for concavity when analyzing maximums and minimums. It helps in confirming whether a point is a local maximum or minimum.

Given the graphed function, find the domain, range, intercepts, local maximums, minimums, intervals of increase/decrease, and end behavior.

Learn how to analyze a graphed function by finding its domain, range, x- and y-intercepts, local maximums and minimums, increasing and decreasing intervals, and end behavior. This exercise is great for high school students studying calculus and advanced algebra.

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