Graph each equation. Begin by filling in the table and...

Graph each equation. Begin by filling in the table and finding five solutions of the equation. Then plot these ordered pairs as points in the rectangular coordinate system and connect the points with a smooth curve.

$$y=\sqrt{x+2}$$
(TABLE CAN'T COPY)

Key Concepts

Plotting Points on the Coordinate Plane

Plotting points involves marking the ordered pairs derived from the table of values onto the rectangular coordinate system. Once enough points are plotted to reflect the behavior of the function, they are connected with a smooth curve to complete the graph. This visual representation helps in understanding the overall shape and behavior of the function.

Domain of a Function

The domain of a function consists of all the input values for which the function is defined. For functions involving square roots, such as the given equation, it is important to set the expression inside the square root greater than or equal to zero. This ensures that the output is a real number, which is essential for correctly determining the graph of the function.

Square Root Functions

Square root functions are those that include a radical with a variable inside it. They have a characteristic shape that starts at a specific point, known as the endpoint, and then increases gradually. Understanding the basic form of a square root function is important for predicting its behavior and for applying any necessary transformations.

Function Transformations

Function transformations involve shifting, stretching, or reflecting the graph of a basic function to produce the graph of a more complex function. In the equation given, adding a constant inside the square root shifts the basic square root function horizontally. Recognizing this transformation helps in accurately plotting the graph using derived points.

Table of Values

A table of values is used to organize a set of input values and their corresponding output values calculated from the function. Creating such a table allows one to systematically compute several ordered pairs, which serve as a guide for plotting the function on the coordinate plane.

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