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Absolute Value Graphs civicpride-kusatsu.net Topical Outline | Algebra 2 Outline | MathBits" Teacher Resources Terms of Use Contact Person: Donna Roberts
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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.

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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.


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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.

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The absolute value function is one of the most recognized piecewise defined functions.


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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 |
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Read more about Absolute Value.
Range: When finding the range of an absolute value function, find the vertex (the turning point). • If the graph opens upwards, the range will be greater than or equal to the y-coordinates of the vertex. • If the graph opens downward, the range will be less than or equal to the y-coordinate of the vertex.

Average rate of change: is constant on each straight line section (ray) of the graph.


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General Form of Absolute Value Function: f (x) = a | x - h | + k • the vertex is at (h,k) • the axis of symmetry is x = h • the graph has a vertical shift of k • the graph opens up if a > 0, down if a


Topical Outline | Algebra 2 Outline | civicpride-kusatsu.net | MathBits" Teacher Resources Terms of Use Contact Person: Donna Roberts