Let's analyze the graph and answer the given questions:

a) Does the graph shown above represent the graph of a function?

To determine if the graph represents a function, use the Vertical Line Test: if any vertical line intersects the graph at more than one point, it is not a function.

From the graph, every vertical line will intersect the curve at only one point. Therefore, Yes, the graph represents a function.

b) Record the domain of the graph. Be sure to write the domain in interval notation.

The domain of a function consists of all the x-values for which the function is defined.

• From the graph, the curve starts from the left side near $x = -4$ and extends to the right, ending at $x = 2$.
• There are no breaks in the graph within this range.

So, the domain in interval notation is: $D = [-4, 2]$

c) Record the range of the graph. Be sure to write the range in interval notation.

The range of a function consists of all the y-values that the function can attain.

• The graph starts from the bottom near $y = -3$ and reaches up to the maximum point at $y = 3$.
• The curve does not go above $y = 3$ or below $y = -3$.

Thus, the range in interval notation is: $R = [-3, 3]$

Would you like further explanations, or do you have any questions?

Related Questions:

1. How do you determine if a graph represents a function using the Vertical Line Test?
2. What are the key steps to find the domain of a function from its graph?
3. How can the range of a function be affected by transformations such as shifts and reflections?
4. What does interval notation mean, and how is it used in mathematics?
5. How can we find the maximum and minimum values of a function graphically?

Tip: To identify the range and domain accurately, focus on the farthest left, right, top, and bottom points of the graph.