Let's analyze the graph based on the given questions and the image you've uploaded:

Part 1: Domain and Range

• Domain: The domain of a function consists of all possible x-values where the function is defined. Based on the graph, it seems the function is defined from $x = -8$ to $x = 8$, as the graph does not extend beyond this interval, and there are open circles at the endpoints.

  Thus, the domain is $(-8, 8)$.

• Range: The range consists of all possible y-values that the function takes. The graph reaches a minimum y-value around $-9$ and a maximum y-value of about 8.

  Therefore, the range is approximately $[-9, 8]$.

Part 2: Y-Intercept

The y-intercept is where the function crosses the y-axis (i.e., where $x = 0$). Based on the graph, the function does not cross the y-axis at any point, as it passes below $y = 0$.

• Hence, Option B: There is no y-intercept.

Part 3: X-Intercepts

The x-intercepts are the points where the function crosses the x-axis (i.e., where $y = 0$).

• From the graph, the function crosses the x-axis around $x = -7$ and $x = 5$.

Thus, the x-intercepts are $x = -7, 5$.

Part 4: Increasing Intervals

A function is increasing where the graph moves upwards as x increases.

• Based on the graph, the function is increasing on the interval $(-8, -4)$ and again on $(2, 6)$.

Part 5: Decreasing Intervals

A function is decreasing where the graph moves downwards as x increases.

• The function is decreasing on the intervals $(-4, 2)$ and $(6, 8)$.

Part 6: Constant Intervals

A function is constant where the graph is flat, meaning it neither increases nor decreases. There are no intervals where the function is constant.

• Option B: The function is not constant on any interval.

Part 7: Relative Extrema

• The function has a relative maximum at approximately $(6, 8)$, where the graph reaches a local peak.
• The function has a relative minimum at approximately $(-4, -9)$, where the graph reaches a local trough.

Part 8: Even, Odd, or Neither

To check if a function is even, odd, or neither:

• Even functions are symmetric with respect to the y-axis.
• Odd functions are symmetric with respect to the origin.

Based on the graph, the function does not exhibit symmetry about the y-axis or the origin, so the function is neither even nor odd.

Would you like to dive deeper into any of the sections? Here are some relative questions:

1. What would the function's graph look like if it had a y-intercept?
2. Can a function have both even and odd properties?
3. How can we find the exact values of the extrema points?
4. How would the graph look if the function were constant on an interval?
5. What happens to the symmetry if a function is shifted horizontally?

Tip: For checking whether a function is odd or even, substitute $f(-x)$ into the function and compare it to $f(x)$ and $-f(x)$.