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What is the domain and range in interval notation of the following graph?

From the graph provided, I can see that it represents a parabola that opens downwards.

### Domain:
- The domain of the graph is the set of all possible \(x\)-values that the graph covers. Since this is a parabola that extends indefinitely to the left and right, the domain includes all real numbers.

In interval notation, the domain is:
\[
(-\infty, \infty)
\]

### Range:
- The range is the set of all possible \(y\)-values. The highest point of the parabola occurs at the vertex, which appears to be at approximately \(y = 4\), and since the parabola opens downward, the \(y\)-values decrease from this point.

In interval notation, the range is:
\[
(-\infty, 4]
\]

Would you like more details, or do you have any other questions?

### Related Questions:
1. What is the equation of this parabola?
2. How do you find the vertex of a parabola from its graph?
3. What are the roots (or x-intercepts) of this parabola?
4. How can we determine the axis of symmetry from the graph?
5. What is the significance of the vertex in terms of maximum and minimum values?

### Tip:
For a quadratic function \(y = ax^2 + bx + c\), the vertex can be found using the formula \(x = -\frac{b}{2a}\), and this helps in determining the range of the function.

What is the domain and range in interval notation of the following graph?

This guide explains how to determine the domain and range of a parabola from its graph. The solution covers key concepts in quadratic functions, including identifying the domain as all real numbers and the range based on the vertex of the parabola.

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