Examine the graph.

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What is the domain and range of the function represented by the graph?

Select two answers: one for the domain and one for the range.

Responses

range: (−∞,∞)

range: (−∞,∞)

range: (−2,4)

range: open paren negative 2 comma 4 close paren

domain: (−2,4)

domain: open paren negative 2 comma 4 close paren

domain: [−9,∞)

domain: [−9,∞)

domain: (−∞,∞)

domain: (−∞,∞)

range: [−9,∞)

range: 

To determine the domain and range of the function represented by the graph, let's break it down:

### Given:
- The graph represents an upward-opening parabola with a vertex at \((1, -16)\).
- The parabola intersects the X-axis at points \((-3, 0)\) and \((5, 0)\).

### **Domain:**
- The domain of a function is the set of all possible values of \(x\) for which the function is defined.
- Since the parabola opens upward and extends infinitely to the left and right, the function is defined for all real numbers.
- **Thus, the domain is \( \textbf{(-∞, ∞)} \)**.

### **Range:**
- The range of a function is the set of all possible values of \(y\) that the function can take.
- The vertex of the parabola is at \((1, -16)\), and since the parabola opens upward, the smallest value of \(y\) is \(-16\).
- The function takes all values of \(y\) greater than or equal to \(-16\).
- **Thus, the range is \( \textbf{[-16, ∞)} \)**.

### Correct Responses:
1. **Domain: \( \textbf{(-∞, ∞)} \)**
2. **Range: \( \textbf{[-16, ∞)} \)**

These are the correct choices for the domain and range.

Do you have any questions or need further details?

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**Related Questions:**
1. How do you determine the domain of more complex functions?
2. What does it mean for a parabola to have a domain of \( (-∞, ∞) \)?
3. How can you find the range of a function without graphing it?
4. What are the implications of a parabola having a minimum or maximum value?
5. How do vertical shifts affect the range of a parabola?

**Tip:** The domain of a parabola that opens up or down is always \( (-∞, ∞) \), but its range depends on the vertex.

Explore how to determine the domain and range of a function from its graph. Learn the concepts of domain and range through an example of an upward-opening parabola. Suitable for students in Grades 9-12.

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