The graph provided shows a piecewise function with one part decreasing sharply before leveling off, then increasing again.

1. Domain:

The domain of a function refers to all possible input values (x-values) that the function can take. From the graph:

• The function appears to extend infinitely to the left but is cut off sharply on the right side, indicating the function exists only up to a certain point.
• The function seems to be defined from $x = -\infty$ to some positive value (likely around 2 or 3).

In interval notation, the domain is approximately: $(-\infty, 3]$

2. Range:

The range of a function refers to all possible output values (y-values) that the function can produce. From the graph:

• The lowest point of the graph seems to occur around $y = -2$.
• The function increases and decreases beyond this, extending upwards but not going below $y = -2$.

In interval notation, the range is approximately: $[-2, \infty)$

Thus, the domain is $(-\infty, 3]$ and the range is $[-2, \infty)$.

Do you need further details or explanations?

Here are 5 related questions:

1. How would the domain change if the graph were shifted left or right?
2. What would happen to the range if the graph were shifted up or down?
3. How can you determine the domain and range of a function without a graph?
4. How do the endpoints of the graph influence the interval notation?
5. How could this graph represent a real-world scenario?

Tip: Always check both ends of a graph when determining the domain and range, especially if they go to infinity.