Absolute worth Graphs snucongo.org Topical outline | Algebra 2 overview | MathBits" Teacher sources Terms that Use call Person: Donna Roberts
We understand that the absolute value of a number is always positive (or zero).
We deserve to see this same an outcome reflected in the graph that the absolute worth parent function y = | x |. All of the graph"s y-values will be hopeful (or zero).
The graph the the absolute worth parent role is composed of two linear "pieces" joined with each other at a common vertex (the origin). The graph that such absolute value attributes generally take away the form of a V, or an up-side-down V. An alert that the graph is symmetric about the y-axis.
Linear "pieces" will show up in the equation that the absolute value role in the adhering to manner: y = | mx + b | + c where the crest is (-b/m, c) and the axis of the opposite is x = -b/m.
note that the slope of the straight "pieces" space +1 top top the best side and also -1 ~ above the left side. Mental that as soon as lines are perpendicular (form a best angle) their slopes are an adverse reciprocals.
attributes (of parent function): • Domain: All Reals (-∞,∞) unless domain is altered. • Range: <0,∞) • increasing (0, ∞) • to decrease (-∞,0)
• positive (-∞, 0) U (0, -∞)
• absolute/relative min is 0 • no pure max (graph → ∞)
x-intercept: intersects x-axis in ~ (0, 0) unless transformed
y-intercept: intersects y-axis at (0, 0) unless reinvented
Vertex: the allude (0,0) unless transformed
Table: Y1: y = | x |
Average price of change: is constant on each straight line section (ray) of the graph.
General type of Absolute worth Function: f (x) = a | x - h | + k • the crest is at (h,k) • the axis of the opposite is x = h • the graph has a vertical shift of k • the graph opens up if a > 0, under if a
Topical overview | Algebra 2 overview | snucongo.org | MathBits" Teacher sources Terms the Use call Person: Donna Roberts