The function shown in the graph is a parabola opening upwards. Let's determine its domain and range:

Domain:

The domain of a function is the set of all possible values for the independent variable (in this case, the $x$-values) for which the function is defined.

• From the graph, the function extends infinitely to the left and right along the $x$-axis. This indicates that there are no restrictions on the values of $x$, meaning the function is defined for all real numbers.

Thus, the domain in interval notation is: $(-\infty, \infty)$

Range:

The range of a function is the set of all possible values of the dependent variable (the $y$-values) that the function can take.

• The lowest point of the parabola is at $y = -1$, and the parabola opens upwards, so the function takes values starting from $-1$ and continues increasing without bound.

Thus, the range in interval notation is: $[-1, \infty)$

Let me know if you'd like more details or explanations.

Here are 5 related questions to deepen your understanding:

1. How does the shape of the parabola determine its domain and range?
2. What are the vertex and axis of symmetry of this parabola?
3. How would the domain and range change if the parabola opened downward?
4. Can a function have a restricted domain but an unrestricted range? Why or why not?
5. How do you find the range of a function without graphing it?

Tip: For quadratic functions like this one, the vertex often provides crucial information about the range.