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.