I see that you've uploaded an image of a worksheet focused on identifying the domain and range of various functions. I'll analyze the image and provide you with details on solving these types of problems.

Let's break down the key concepts for identifying the domain and range of the functions depicted:

1. Domain:

• The domain of a function refers to all the possible input values (x-values) that the function can accept. For most graphs, this corresponds to the x-values that are covered by the graph from left to right.

2. Range:

• The range of a function refers to all the possible output values (y-values) that the function can produce. This corresponds to the y-values covered by the graph from bottom to top.

General Steps to Determine Domain and Range from a Graph:

• Domain: Look at the graph and determine the span of x-values covered by the graph.

  • For instance, if the graph stretches from x = -2 to x = 3, the domain is $[-2, 3]$.
  • If there are any breaks or holes in the graph, consider these when determining the domain.

• Range: Look at the graph and determine the span of y-values covered by the graph.

  • For example, if the graph goes from y = -1 to y = 4, the range is $[-1, 4]$.
  • Like with the domain, take note of any gaps or breaks.

Example Analysis:

Let's take a specific example from your worksheet:

1. Top Left Graph:
   • Domain: This will likely involve identifying the leftmost and rightmost points on the graph.
   • Range: Look for the lowest and highest points the graph reaches on the y-axis.

If you want me to go through the entire worksheet and provide the domain and range for each function, I can do that step by step. Would you like to proceed with that, or do you have specific questions about certain graphs?

5 Related Questions You Might Consider:

1. What is the domain and range of a quadratic function?
2. How do you determine the domain and range for piecewise functions?
3. Can you explain how to identify domain and range for functions with asymptotes?
4. How does the concept of domain and range apply to trigonometric functions?
5. What happens to the domain and range when a function is reflected or translated?

Tip:

Always check for open and closed circles on the graph. Open circles indicate that the point is not included in the domain or range, while closed circles indicate that it is included.