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The graph you provided shows a periodic function that appears to be a sine or cosine wave with multiple oscillations. Let's analyze the graph to determine the domain and range.

### 1. **Domain:**
The graph extends indefinitely in both the positive and negative horizontal directions (along the x-axis). Since there are no restrictions on the x-values in this sine-like function, the domain is all real numbers.

**Domain:** \( (-\infty, \infty) \)

### 2. **Range:**
The function oscillates between a maximum of 4 and a minimum of -4 along the y-axis. This gives us the range of the function.

**Range:** \( [-4, 4] \)

Would you like further clarification or additional details on this?

Here are five related questions to expand your understanding:
1. What type of function is typically associated with oscillating patterns like this graph?
2. How can you determine the period of a periodic function like the one shown?
3. What is the amplitude of this graph, and how is it determined?
4. Can you explain how to find the phase shift of a sine or cosine function from its graph?
5. How would the domain and range change if the amplitude or vertical shift of the function were different?

**Tip:** The range of a periodic function is directly linked to its amplitude, which is the distance from the midline to the peak (or trough) of the wave.

Determine the domain and range of the graph provided.

Analyze a periodic sine function graph to determine its domain and range. Learn how the function oscillates between -4 and 4, with a domain extending from negative to positive infinity. Suitable for high school students studying trigonometry.

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