For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation. y=√(x-3)

Verified step by step guidance

1. Identify the domain of the function \(y = \sqrt{x - 3}\). Since the expression inside the square root must be non-negative, set \(x - 3 \geq 0\), which means \(x \geq 3\).
2. Choose at least three values of \(x\) that satisfy the domain condition (i.e., \(x \geq 3\)). For example, select \(x = 3\), \(x = 4\), and \(x = 7\).
3. Calculate the corresponding \(y\) values by substituting each chosen \(x\) into the equation \(y = \sqrt{x - 3}\). For instance, for \(x=3\), compute \(y = \sqrt{3 - 3}\); for \(x=4\), compute \(y = \sqrt{4 - 3}\); and for \(x=7\), compute \(y = \sqrt{7 - 3}\).
4. Create a table of ordered pairs \((x, y)\) using the values found in the previous step. This table will show at least three points that lie on the graph of the equation.
5. To graph the equation, plot the ordered pairs from the table on the coordinate plane. Then, draw a smooth curve starting at the point where \(x=3\) (the domain's start) and continuing to the right, reflecting the shape of the square root function.

Key Concepts

Domain of a Function

The domain is the set of all input values (x-values) for which the function is defined. For the equation y = √(x - 3), the expression inside the square root must be non-negative, so x - 3 ≥ 0, meaning the domain is x ≥ 3.

Evaluating Functions and Ordered Pairs

To find ordered pairs (x, y) that satisfy the equation, substitute values of x from the domain into the function and calculate the corresponding y-values. These pairs represent points on the graph of the function.

Graphing Square Root Functions

Graphing y = √(x - 3) involves plotting points from the ordered pairs and understanding the shape of the square root function, which starts at the domain boundary (x=3) and increases gradually, forming a curve that rises slowly to the right.