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The square root function is a crucial concept in mathematics, and it involves finding numbers that, when multiplied by themselves, give the original number under the square root symbol. In this exercise, the function given is \(y = \sqrt{5 - x}\). Understanding how this function behaves is essential to solve such problems.

- **Graph Shape:** The standard square root function \(y = \sqrt{x}\) typically produces a curve that starts at the origin and extends to the right, illustrating a continuously increasing function. The curve arcs gently, showing that progress slows as values increase.

- **Horizontal Shift:** In our equation \(y = \sqrt{5 - x}\), the presence of \(5 - x\) shifts the graph horizontally by 5 units to the left. This changes where the graph starts, affecting which coordinate points lie on it.

Getting comfortable with how square root functions transform with simple operations like addition, subtraction, and operations inside the square root will aid in quickly evaluating any point.

Coordinate points are pairs of numbers that define the position of a point on a plane. It's like having coordinates as specific addresses telling us exactly where something is located.

- **Understanding the Plane:** The horizontal number line represents the x-values and the vertical number line represents the y-values. Together, these form a two-dimensional grid where any point is represented as (x, y).

- **Evaluating Points on a Curve:** To determine if a point lies on the graph of \(y = \sqrt{5 - x}\), substitute the x-value into the equation and check if resulting y-value matches the y-coordinate of the given point.

Using coordinate points helps us visualize and understand how different values relate in a function and provides a strong foundation for evaluating equations.

Evaluating an equation means substituting the given values into the equation to verify their validity.

- **Practical Steps to Evaluate:** Consider a point with coordinates (x, y). To see if this point is on the graph of \(y = \sqrt{5 - x}\), you replace \(x\) and \(y\) in the equation with 1 and 2, respectively, for example. Check if both sides reflect equal values.

- **Example Calculation:** For the point \((1, 2)\), the substitution changes the equation to \(2 = \sqrt{5 - 1}\), simplifying to \(2 = \sqrt{4}\), ultimately verifying with \(2 = 2\).

- **Conclusion:** If both sides equal each other after these substitutions, the original coordinate point lies on the graph, confirming its place within the function’s set of solutions.

By practicing evaluation, you develop intuitive understanding and skill in manipulating variables and numbers, empowering you to tackle diverse algebraic challenges effectively.