**Absolute Value Graphs**civicpride-kusatsu.net Topical Outline | Algebra 2 Outline | MathBits" Teacher Resources

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We know that the absolute value of a number is always positive (or zero). We can see this same result reflected in the graph of the absolute value parent function 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 Linear "pieces" will appear in the equation of the absolute value function in the following manner: | 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. |

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 |

*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.

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