Absolute value Graphs civicpride-kusatsu.net Topical synopsis | Algebra 2 overview | MathBits" Teacher sources Terms of Use contact Person: Donna Roberts

We recognize that the absolute worth of a number is always positive (or zero).

You are watching: Which describes the range of the parent absolute value function?

We deserve to see this same an outcome 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 that the absolute worth parent role is written of two direct "pieces" joined with each other at a common vertex (the origin). The graph of such absolute value functions generally bring away the form of a V, or one up-side-down V. An alert that the graph is symmetric about the y-axis.

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Linear "pieces" will appear in the equation the the pure value role in the complying with manner: y = | mx + b | + c where the vertex is (-b/m, c) and also the axis of the contrary is x = -b/m.

note that the steep of the straight "pieces" space +1 on the ideal side and also -1 ~ above the left side. Psychic that when lines room perpendicular (form a ideal angle) your slopes are negative reciprocals.

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


attributes (of parent function): Domain: All Reals (-∞,∞) unless domain is altered. • Range: <0,∞) increasing (0, ∞) • decreasing (-∞,0)

• confident (-∞, 0) U (0, -∞)

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

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

y-intercept: intersects y-axis in ~ (0, 0) unless changed

Vertex: the suggest (0,0) unless changed

Table: Y1: y = | x |
Read an ext about pure Value.
Range: once finding the selection of an absolute value function, discover the crest (the turning point). • If the graph opens upwards, the selection will be higher than or equal to the y-coordinates the the vertex. • If the graph opens downward, the variety will be much less than or same to the y-coordinate that the vertex.

Average price of change: is continuous on each straight line ar (ray) that the graph.


General type of Absolute worth Function: f (x) = a | x - h | + k • the crest is in ~ (h,k) • the axis of symmetry is x = h • the graph has a vertical shift of k • the graph opens up up if a > 0, under if a

Topical outline | Algebra 2 summary | civicpride-kusatsu.net | MathBits" Teacher resources Terms of Use contact Person: Donna Roberts