Graph each function. See Examples 6 – 8. ƒ(x) = √-x

Key Concepts

Domain of a Function

The domain of a function refers to the set of all possible input values (x-values) for which the function is defined. For the function ƒ(x) = √-x, the expression under the square root must be non-negative, meaning -x ≥ 0 or x ≤ 0. This indicates that the function is only defined for x-values less than or equal to zero.

Graphing Square Root Functions

Graphing square root functions involves plotting points based on the function's output for given inputs. For ƒ(x) = √-x, the graph will consist of points where x is non-positive, and the output will be real numbers. The graph will start at the origin (0,0) and extend leftward, forming a curve that rises as x approaches zero.

Transformations of Functions

Transformations of functions involve shifting, reflecting, stretching, or compressing the graph of a function. In the case of ƒ(x) = √-x, the negative sign indicates a reflection across the y-axis compared to the standard square root function ƒ(x) = √x. Understanding these transformations helps in accurately sketching the graph based on the original function.