https://file.aiquickdraw.com/mathbot/file/1725839834410sji5yd8x.jpg

​(c) If the graph is that of a​ function, determine what kinds of symmetry it has. Select all that apply.
A.
It is symmetric with respect to the​ y-axis.
B.
It is symmetric with respect to the origin.
C.
It is symmetric with respect to the​ x-axis.
D.
The graph is not symmetric with respect to the​ x-axis, y-axis, or the origin.
E.
The graph is not a function.

The graph shows a parabola, which appears to be symmetric with respect to the y-axis. We can determine this by observing that the graph is a U-shape centered at \( x = -4 \), meaning the left and right sides of the parabola are mirror images across the vertical line passing through \( x = -4 \).

### Symmetry:
- **A. Symmetric with respect to the y-axis:** 
  No, because the parabola is not centered at \( x = 0 \) (the y-axis); it is centered at \( x = -4 \).

- **B. Symmetric with respect to the origin:** 
  No, the graph does not have origin symmetry (it is not reflected through the origin).

- **C. Symmetric with respect to the x-axis:** 
  No, parabolas generally do not have symmetry across the x-axis unless they are horizontal parabolas, which this is not.

- **D. The graph is not symmetric with respect to the x-axis, y-axis, or the origin:** 
  Correct, this graph is not symmetric about these axes or the origin.

- **E. The graph is not a function:** 
  No, the graph represents a parabola, which is a function. The graph passes the vertical line test, meaning it is indeed a function.

### Conclusion:
The correct answer is **D**: The graph is not symmetric with respect to the x-axis, y-axis, or the origin.

Would you like more details on the concept of symmetry or have any other questions?

### Related questions:
1. What is the general form of the equation of a parabola with symmetry around a different vertical line?
2. How do you check for symmetry with respect to the y-axis?
3. Can a function be symmetric with respect to the origin and still be a function?
4. What are the characteristics of parabolas that are symmetric about the x-axis?
5. How does the vertical line test help to determine if a graph represents a function?

**Tip:** The symmetry of a function can be quickly identified by its equation. For example, a quadratic function \( y = ax^2 + bx + c \) is symmetric with respect to a vertical line determined by its vertex.

If the graph is that of a function, determine what kinds of symmetry it has. Select all that apply.

This problem asks about the symmetry of a quadratic function graph, focusing on key concepts like the vertical line test, y-axis symmetry, and identifying whether the function is symmetric with respect to the x-axis or origin. Suitable for students in Grades 9-11.

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