The graph of an absolute value function opens down and has a vertex of (0, -3).The domain of the function is .The range of the function is .

An absolute value function typically takes the form $f(x) = a |x - h| + k$, where $(h, k)$ represents the vertex and $a$ indicates the direction of the opening of the graph. In this case, since the graph opens down, we know that $a$ must be negative.

1. Understanding the Vertex

Given that the vertex is at $(0, -3)$, we can state:

• $h = 0$
• $k = -3$

2. Form of the Function

Since the function opens downward, $a$ should be negative. Therefore, the function can be written as: $f(x) = -a |x| - 3$ for some positive value of $a$.

3. Determining the Domain

The domain of an absolute value function is always all real numbers. Therefore:

• Domain: $(-\infty, \infty)$

4. Determining the Range

The vertex indicates the maximum value of the function, which is $-3$, as the graph opens downward. Thus, the range will be all values less than or equal to $-3$:

• Range: $(-\infty, -3]$

Final Answer

• Domain: $(-\infty, \infty)$
• Range: $(-\infty, -3]$