Graph each function. See Examples 1 and 2. h(x) = |-½ x|

Key Concepts

Absolute Value Function

The absolute value function, denoted as |x|, outputs the non-negative value of x. This means that for any real number input, the function will return the distance of that number from zero on the number line, effectively removing any negative sign. Understanding this function is crucial for graphing h(x) = |-½ x|, as it will affect the shape and position of the graph.

Transformation of Functions

Transformations involve altering the basic shape of a function through shifts, stretches, or reflections. In the case of h(x) = |-½ x|, the factor of -½ indicates a horizontal stretch by a factor of 2 and a reflection across the y-axis. Recognizing these transformations helps in accurately sketching the graph of the function based on its parent function.

Graphing Techniques

Graphing techniques involve plotting points and understanding the behavior of functions to create accurate visual representations. For h(x) = |-½ x|, it is essential to identify key points, such as where the function equals zero and its behavior as x approaches positive and negative infinity. Mastery of these techniques allows for a clear and precise graph of the function.