Graph each function. ƒ(x) = -|x|

Key Concepts

Absolute Value Function

The absolute value function, denoted as |x|, outputs the non-negative value of x regardless of its sign. This means that for any real number x, |x| is equal to x if x is positive or zero, and -x if x is negative. Understanding this function is crucial for graphing transformations, as it forms the basis for the shape of the graph.

Transformation 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 over the x-axis. This concept is essential for predicting how the graph of a function will change based on modifications to its equation.

Graphing Techniques

Graphing techniques involve plotting points and understanding the shape and behavior of functions on a coordinate plane. For ƒ(x) = -|x|, the graph will form a 'V' shape that opens downward, with its vertex at the origin (0,0). Mastery of graphing techniques allows for accurate visual representation and analysis of functions.