https://r2.erweima.ai/mathbot/image/17246967098534r05yz1t.jpg

i) The domain is:      

     ii) The range is:

The graph in the image is a parabola that opens upwards, indicating a quadratic function. Let's determine the domain and range based on the graph:

### i) Domain:
The domain of a function is the set of all possible input values (x-values) for which the function is defined. For a quadratic function (which forms a parabola), the domain is all real numbers because the parabola extends infinitely to the left and right.

**Domain:** \( \mathbb{R} \) or \((- \infty, \infty)\)

### ii) Range:
The range of a function is the set of all possible output values (y-values). Since the parabola opens upwards and has a minimum point (vertex), the range starts from the y-coordinate of the vertex and extends upwards to infinity.

**Range:** Based on the graph, the vertex appears to be at \( y = 0 \), so the range is \( y \geq 0 \).

**Range:** \( [0, \infty) \)

Would you like more details or have any questions?

### Related Questions:
1. What is the vertex of the parabola?
2. How do you find the axis of symmetry of a quadratic function?
3. What is the standard form of a quadratic equation?
4. How can you determine if a parabola opens upwards or downwards?
5. What are the roots of the quadratic function shown?

### Tip:
When analyzing the domain and range of functions, sketching or visualizing the graph can significantly help in understanding the behavior of the function.

Learn how to determine the domain and range of quadratic functions with detailed explanations and graphs. Understand why the domain of a quadratic function is all real numbers and how the range is affected by the direction of the parabola. Suitable for high school students.

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