Graph each function. ƒ(x) = |x| -3

Key Concepts

Absolute Value Function

The absolute value function, denoted as |x|, measures the distance of a number x from zero on the number line, always yielding a non-negative result. This function has a V-shaped graph that opens upwards, with its vertex at the origin (0,0). Understanding this function is crucial for graphing ƒ(x) = |x| - 3, as it influences the overall shape and position of the graph.

Vertical Shifts

Vertical shifts occur when a function is adjusted up or down by adding or subtracting a constant from the function's output. In the function ƒ(x) = |x| - 3, the '-3' indicates a downward shift of the entire graph by three units. This concept is essential for accurately positioning the graph of the function relative to the standard absolute value function.

Graphing Techniques

Graphing techniques involve plotting points and understanding the behavior of functions to create accurate visual representations. For ƒ(x) = |x| - 3, one can start by plotting key points, such as the vertex at (0, -3), and then using the properties of the absolute value function to extend the graph symmetrically. Mastery of these techniques is vital for effectively visualizing and interpreting the function.