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The graph you provided appears to represent a continuous function that extends indefinitely in both the left and right directions on the x-axis, suggesting it is a function that covers all real numbers as its domain. Therefore, the domain of the function \( f(x) \) is:

\[ \text{Domain: all real numbers} \]

Looking at the y-values, the function reaches a minimum point and then rises indefinitely as it moves further along the x-axis in both directions. This suggests that the minimum y-value is the lowest point on the graph. This point appears to be around \( y = 1 \), and since the function rises without bound, the range of the function starts at this minimum y-value and extends to infinity. Thus, the range of the function \( f(x) \) is:

\[ \text{Range: } y \geq 1 \]

Do you have any specific questions about this explanation, or is there anything else you'd like to know about functions and their properties?

Here are some additional questions you might consider:
1. What would the function look like if it had a finite domain?
2. How does changing the coefficients of a function affect its graph?
3. Can a function have more than one minimum or maximum point?
4. What are some real-world applications of understanding the domain and range of functions?
5. How do restrictions on the domain affect the range of a function?

**Tip:** When studying functions, always consider the behavior at the extremes (very large or very small values of \( x \)) to fully understand the domain and range.

This problem involves finding the domain and range of a quadratic function represented by a parabola. The domain includes all real numbers, and the range starts from the minimum y-value (y ≥ 1). This question helps students understand key concepts in quadratic functions and is suitable for students in Grades 8-10.

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