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Write the domain and range of each function. Write your answers in interval notation

The graph you've provided appears to represent a parabola.

### Domain
The domain of a function is the set of all possible input values (x-values) for which the function is defined. For parabolas that extend infinitely to the left and right, the domain includes all real numbers.

**Domain:** \((- \infty, \infty)\)

### Range
The range of a function is the set of all possible output values (y-values). For this parabola, the vertex is at the highest point on the graph, which looks to be around \( y = 4 \). The parabola opens downward, meaning the range includes all real numbers from \(-\infty\) up to the vertex's y-coordinate.

**Range:** \((-\infty, 4]\)

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Would you like more details or have any questions? Here are some related questions that might interest you:

1. How do you determine the vertex of a parabola?
2. How can you identify whether a parabola opens upwards or downwards?
3. What is the standard form of a quadratic equation?
4. How do you find the axis of symmetry for a parabola?
5. What are the implications of the discriminant in a quadratic function?

**Tip:** When analyzing the range of a parabola, always consider whether the parabola opens upwards or downwards, as this determines whether the range starts from the vertex and goes upwards or downwards.

Write the domain and range of each function. Write your answers in interval notation.

This guide provides a detailed solution to determine the domain and range of a parabolic function using interval notation. Suitable for students in Grades 9-12, it covers key algebraic concepts including domain, range, and the properties of parabolas.

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