The graph you uploaded represents an absolute value function, typically expressed as $f(x) = |x|$, but with transformations that alter its appearance. To determine the domain and range:

Domain (D):

The domain of a function represents the set of all possible $x$-values (inputs) for which the function is defined. Since the graph extends indefinitely along the horizontal axis (both left and right), there are no restrictions on $x$.

• Domain (D): $(-\infty, \infty)$ or "all real numbers."

Range (R):

The range represents the set of all possible $y$-values (outputs) the function can take. From the graph, the vertex of the absolute value function occurs at $y = 5$, and the graph moves downward. Therefore, the graph never exceeds $y = 5$, and the lowest point goes towards negative infinity.

• Range (R): $(-\infty, 5]$.

Would you like more details on how the transformations affect the parent function, or any additional clarifications?

Here are 5 follow-up questions related to this concept:

1. What are the transformations applied to the parent function $f(x) = |x|$ in this case?
2. How would you write the equation of this specific absolute value function?
3. How can you determine the vertex of an absolute value function?
4. How do changes in slope affect the graph of an absolute value function?
5. Can the range of an absolute value function ever be infinite?

Tip: The domain of absolute value functions is always all real numbers, but the range depends on the position of the vertex.