To analyze this graph, we need to determine its domain, range, x-intercepts, and y-intercepts.

1. Domain

The domain of a function is the set of all possible x-values. From the graph, it appears that:

• The x-values start around $-2$ and end around $2$.

So, the domain is: $[-2, 2]$

2. Range

The range of a function is the set of all possible y-values. Observing the graph:

• The y-values range from a minimum near $-6$ to a maximum near $2$.

Therefore, the range is: $[-6, 2]$

3. X-Intercepts

The x-intercepts occur where the graph crosses the x-axis (where $y = 0$). From the graph, we see:

• The curve crosses the x-axis at $x = -1$ and $x = 1$.

So, the x-intercepts are: $(-1, 0) \quad \text{and} \quad (1, 0)$

4. Y-Intercept

The y-intercept occurs where the graph crosses the y-axis (where $x = 0$). From the graph:

• The curve crosses the y-axis at $y = 2$.

Thus, the y-intercept is: $(0, 2)$

Would you like more details or have any other questions?

Related Questions

1. How can we determine the behavior of the graph based on its slope changes?
2. What type of function could this graph represent?
3. How do we determine increasing and decreasing intervals from the graph?
4. How could we find the maximum and minimum points of this function?
5. What role do intercepts play in graphing functions?

Tip

When analyzing graphs, always note intercepts and endpoints to help with understanding the function's behavior and domain/range.