For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b

step 1 Using the equation Y is equal to the square root of x minus 3, we're going to plug in the values

For each equation, (a) give a table with at least three...

Key Concepts

Ordered Pairs

Ordered pairs are combinations of x and y values that satisfy a given function. Creating a table with ordered pairs involves selecting x-values from the function's domain, calculating the corresponding y-values, and organizing them into pairs. This process is essential for accurately graphing the function and observing its specific behavior at certain points.

Domain and Range

For functions involving square roots, the domain is restricted by the need for the radicand to be non-negative. In y = sqrt(x-3), the condition x-3 ? 0 leads to a domain of x ? 3. Consequently, since the square root produces non-negative outputs, the range of the function is y ? 0.

Graphing Functions

Graphing a function involves depicting its behavior visually on the Cartesian coordinate system by plotting a series of points that satisfy the function's equation and then connecting them smoothly. For y = sqrt(x-3), a proper graph reflects the horizontal shift and domain restrictions, helping in understanding how algebraic transformations affect the function's geometry.

Square Root Function

A square root function takes a number and returns its principal (non-negative) square root. It is defined only for non-negative numbers, which means that the expression under the square root must be zero or positive. This function is fundamental in algebra and is often used to model various natural phenomena and geometric relationships.

Transformation of Functions

The function y = sqrt(x-3) represents a horizontal shift of the parent square root function y = sqrt(x). In transformations, modifying the input variable (x) inside the function by subtracting or adding a constant shifts the graph horizontally without altering its overall shape.

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