Graph each function. ƒ(x) = -√x - 2

Key Concepts

Square Root Function

The square root function, denoted as √x, is defined for non-negative values of x and produces the principal (non-negative) square root. It is a fundamental function in algebra, characterized by its gradual increase and a domain of [0, ∞). Understanding this function is crucial for graphing transformations, such as reflections and translations.

Transformations of Functions

Transformations involve altering the graph of a function through shifts, stretches, compressions, or reflections. In the function ƒ(x) = -√x - 2, the negative sign indicates a reflection across the x-axis, while the '-2' represents a vertical shift downward by 2 units. Mastery of these transformations is essential for accurately graphing modified functions.

Graphing Techniques

Graphing techniques include plotting points, identifying key features such as intercepts and asymptotes, and understanding the overall shape of the function. For ƒ(x) = -√x - 2, one would start by determining the vertex, which is the lowest point of the graph due to the reflection, and then sketching the curve based on the transformations applied. Proficiency in these techniques is vital for visualizing and interpreting functions.