Students learned in previous courses that absolute value is the distance between a number and 0 on the number line. In this lesson, students look at the function .

Students see that because the graph of the absolute value function is composed of two linear pieces that form a V shape, the same function can also be defined as a piecewise function and described with this equation:

Students also look at basic translations of the absolute value function by considering functions of the forms and .  They focus on the location of the vertex of the graph, which is the highest or lowest point in an area of the graph. After noticing the influence of the constants, an optional activity is available to practice translating absolute value functions.

Students look for and make use of structure (MP7) to relate the translation of a graph to the terms or values in the expression that defines the function. The distinctive V shape of the graph of an absolute value function is ideal for observing how adding or subtracting a constant term affects its graph.