https://file.aiquickdraw.com/mathbot/file/1727021644591umwq6ai9.jpg

The graph provided shows a parabola that opens upwards, centered at the origin. The parabola is a typical representation of a quadratic function, such as \( y = ax^2 \) (with \( a > 0 \)), and the graph passes the vertical line test, confirming that it represents a function.

Let's analyze the given statements:

- **a. "The graph given is not a function."**
  - This is **incorrect** because the graph passes the vertical line test, meaning for every \( x \)-value, there is only one corresponding \( y \)-value.

- **b. "The domain is a set of positive real numbers."**
  - This is **incorrect**. The domain of the function is all real numbers (\( (-\infty, \infty) \)), since the parabola extends infinitely in both directions along the \( x \)-axis.

- **c. "The codomain is the set of positive real numbers."**
  - This is **incorrect**. The codomain (or range) of the function includes all real numbers greater than or equal to 0, but not strictly positive real numbers. The parabola has a minimum value at \( y = 0 \), so the codomain is \( [0, \infty) \).

- **d. "The domain and codomain are set of positive real numbers."**
  - This is **incorrect** for both the domain and codomain. As mentioned earlier, the domain is all real numbers, and the codomain is \( [0, \infty) \).

Thus, **none of the options provided are entirely correct** based on the analysis.

Let me know if you want further details or explanations! Here are 5 related questions to expand your understanding:

1. What is the domain of a quadratic function in general?
2. How do you determine if a graph represents a function?
3. What is the significance of the vertical line test for functions?
4. How can you find the range of a quadratic function from its graph?
5. How would the graph change if the parabola opened downwards?

**Tip:** The domain of a function represents all possible inputs (x-values), while the codomain (range) represents all possible outputs (y-values). Always check both carefully when interpreting graphs.

For the above graph, which one of the following statements is correct?

a. The graph given is not a function.
b. The domain is a set of positive real numbers.
c. The codomain is the set of positive real numbers.
d. The domain and codomain are set of positive real numbers.

Understand how to determine the domain and codomain of a quadratic function using the graph of a parabola. This problem involves key concepts in algebra and functions, suitable for students in Grades 9-12.

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