You have two functions here: 

1. \( f(x) = x \), which is a linear function where the output is equal to the input.
2. \( g(x) = x^2 \), which is a quadratic function, and the output is the square of the input.

The domain for both functions is given as \( 0 \leq x \leq 10 \), meaning the functions are only defined for values of \( x \) between 0 and 10, inclusive.

### Graphical Representation:
- \( f(x) = x \) is a straight line passing through the origin with a slope of 1.
- \( g(x) = x^2 \) is a parabola opening upwards, with its vertex at the origin.

### Calculating a few values:
For \( f(x) \):
- \( f(0) = 0 \)
- \( f(5) = 5 \)
- \( f(10) = 10 \)

For \( g(x) \):
- \( g(0) = 0^2 = 0 \)
- \( g(5) = 5^2 = 25 \)
- \( g(10) = 10^2 = 100 \)

Would you like to see a graph of these functions or any further details?

### Relative Questions:
1. How does the slope of \( f(x) = x \) compare with other linear functions?
2. What are the main characteristics of a quadratic function like \( g(x) = x^2 \)?
3. How does the domain \( 0 \leq x \leq 10 \) affect the range of both functions?
4. What happens if you combine \( f(x) \) and \( g(x) \) into a new function \( h(x) = f(x) + g(x) \)?
5. How can we interpret the intersection points of these two functions graphically?

**Tip:** In quadratic functions like \( g(x) = x^2 \), the shape of the graph is always symmetrical about the vertex.

Explore the comparison between the linear function f(x) = x and the quadratic function g(x) = x^2 over the domain 0 <= x <= 10. This solution includes graph representations, key values for both functions, and insights into the differences in their behavior. Ideal for students in Grades 7-9.

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