Let's analyze the problem step by step.

Step 1: Determine if the graph represents a function

The vertical line test states that a graph represents a function if and only if every vertical line intersects the graph at most once. From the image:

• The graph appears to be a curved arc.
• Any vertical line drawn on this graph will intersect it at most one point.

Thus, the graph does represent a function. The correct answer is B: Yes, because every vertical line can intersect the graph in at most one point.

Step 2: Analyze the graph

(a) Domain and Range:

• Domain: The horizontal extent of the graph. From the graph, the x-values range from $-4$ to $4$, inclusive.
  • Domain: $[-4, 4]$
• Range: The vertical extent of the graph. From the graph, the y-values range from $0$ to $4$, inclusive.
  • Range: $[0, 4]$

(b) Intercepts:

• x-intercept: The graph crosses the x-axis at $(0, 0)$.
• y-intercept: The graph also crosses the y-axis at $(0, 0)$.

Thus, the intercepts are $(0, 0)$.

(c) Symmetry:

• The graph is symmetric about the y-axis, as the left and right halves are mirror images.

Final Answer:

1. The graph represents a function.
2. Domain: $[-4, 4]$
3. Range: $[0, 4]$
4. Intercepts: $(0, 0)$
5. Symmetry: Symmetric with respect to the y-axis.

Do you have any questions or need further clarification?

Here are five related questions for practice:

1. What is the domain of a function if its graph spans all x-values except $x = 2$?
2. How do you determine symmetry with respect to the origin?
3. If a graph fails the vertical line test, what does it represent?
4. Can a function have more than one y-intercept? Why or why not?
5. How would the range change if the graph extended upward to $y = 6$?

Tip: Always verify a graph’s symmetry by substituting $-x$ or $-y$ into the function’s equation (if available).