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).

You are watching: Which of the following are characteristics of the graph of the absolute value parent function

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.

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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.

The pure value duty is among the most well-known piecewise identified functions.


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 |
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Range: as soon as finding the range of an absolute worth function, find the vertex (the transforming point). • If the graph opens up upwards, the selection will be greater than or equal to the y-coordinates the the vertex. • If the graph opens up downward, the range will be less than or same to the y-coordinate of the vertex.

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