Step 1: Determine Whether the Graph is a Function

To determine if the given graph represents a function, we apply the Vertical Line Test:

• The test states that if a vertical line intersects a graph at more than one point anywhere, then the graph is not a function.
• From the given description, vertical lines such as $x = 7$ intersect the graph at two points.
• This confirms that the graph fails the vertical-line test.

Thus, the correct answer is:
A. No, the graph is not a function because a vertical line $x = 7$ intersects the graph at two points. ✅

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Step 2: Find the Domain and Range

The domain represents all possible $x$-values the graph covers, while the range represents all possible $y$-values.

• The given graph consists of two branches opening left and right.
• The left branch starts at $x = -5$ and extends left indefinitely.
• The right branch starts at $x = 5$ and extends right indefinitely.

Thus, the domain is:
$(-\infty, -5] \cup [5, \infty)$

• The highest and lowest points on the graph occur at $y = \pm 6.6$, meaning the range includes all $y$-values from $-6.6$ to $6.6$.

Thus, the range is:
$[-6.6, 6.6]$

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Step 3: Find the Intercepts

$x$-Intercepts:

• The graph intersects the $x$-axis at points $(-5,0)$ and $(5,0)$.
• These are the $x$-intercepts.

$y$-Intercepts:

• The graph does not cross the $y$-axis, so there are no $y$-intercepts.

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Step 4: Check for Symmetry

A graph may have symmetry with respect to:

1. The $x$-axis (if replacing $y$ with $-y$ gives the same equation).
2. The $y$-axis (if replacing $x$ with $-x$ gives the same equation).
3. The Origin (if replacing $x$ with $-x$ and $y$ with $-y$ gives the same equation).

Observing the graph:

• The left and right branches are mirror images across the $y$-axis.
• This means the graph has y-axis symmetry.

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Final Answers:

1. Is it a function? No, the vertical-line test fails. ✅
2. Domain: $\mathbf{(-\infty, -5] \cup [5, \infty)}$ ✅
3. Range: $\mathbf{[-6.6, 6.6]}$ ✅
4. Intercepts: $x$-intercepts: $(-5,0)$ and $(5,0)$; no $y$-intercepts. ✅
5. Symmetry: y-axis symmetry. ✅

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Would you like a more detailed explanation on any part?

Here are some related questions to explore:

1. How can you determine symmetry algebraically?
2. What are the conditions for a graph to pass the vertical-line test?
3. What happens if the graph had an additional branch intersecting the y-axis?
4. How do we express domain and range correctly in interval notation?
5. What other types of symmetry exist in mathematics?

💡 Tip: If a graph is symmetric with respect to the y-axis, its equation remains unchanged when $x$ is replaced with $-x$.