 Absolute Value Graphs civicpride-kusatsu.net Topical Outline | Algebra 2 Outline | MathBits" Teacher Resources Terms of Use Contact Person: Donna Roberts We know that the absolute value of a number is always positive (or zero).You are watching: Which describes the range of the parent absolute value function? We can see this same result reflected in the graph of the absolute value parent function y = | x |. All of the graph"s y-values will be positive (or zero). The graph of the absolute value parent function is composed of two linear "pieces" joined together at a common vertex (the origin). The graph of such absolute value functions generally takes the shape of a V, or an up-side-down V. Notice that the graph is symmetric about the y-axis.See more: What Kind Of Mattress Does Holiday Inn Use, Holiday Inn Simmons Beautyrest Hotel Mattress Linear "pieces" will appear in the equation of the absolute value function in the following manner: y = | mx + b | + c where the vertex is (-b/m, c) and the axis of symmetry is x = -b/m. Note that the slope of the linear "pieces" are +1 on the right side and -1 on the left side. Remember that when lines are perpendicular (form a right angle) their slopes are negative reciprocals. The absolute value function is one of the most recognized piecewise defined functions.  Features (of parent function): Domain: All Reals (-∞,∞) Unless domain is altered. • Range: <0,∞) increasing (0, ∞) • decreasing (-∞,0)

• positive (-∞, 0) U (0, -∞)

• absolute/relative min is 0 • no absolute max (graph → ∞)

x-intercept: intersects x-axis at (0, 0) unless transformed

y-intercept: intersects y-axis at (0, 0) unless transformed

Vertex: the point (0,0) unless transformed

Table: Y1: y = | x |  