To determine the interval notation for the domain and range of the graph in the image, let's break down the analysis:

1. Domain:

• Observation: The graph extends horizontally in both directions along the x-axis.
• Interpretation: Since this is likely a trigonometric function, such as a sine or cosine function, which are continuous and periodic, the domain includes all real numbers.
• Interval Notation: The domain is $(-\infty, \infty)$

2. Range:

• Observation: The graph oscillates between a maximum and minimum value vertically on the y-axis. It appears to reach a maximum value of approximately 2 and a minimum value of approximately -2.
• Interpretation: The range of the function is the set of all y-values that the graph attains.
• Interval Notation: The range is $[-2, 2]$

So, the interval notation for the domain and range of the graph is:

• Domain: $(- \infty, \infty)$
• Range: $[-2, 2]$

Would you like more details or have any questions?

Related Questions:

1. How do you determine the domain of a trigonometric function?
2. What are the typical ranges for sine and cosine functions?
3. How can phase shift affect the domain and range of a function?
4. What transformations can change the range of a trigonometric function?
5. How do vertical and horizontal shifts impact the graph of a trigonometric function?
6. Can the range of a sine or cosine function be altered by changing the amplitude?
7. How does the period of a function relate to its domain?
8. What is the significance of symmetry in determining the range of trigonometric functions?

Tip: When analyzing trigonometric functions, always start by identifying the amplitude, period, and any shifts in the function, as these will directly influence the domain and range.