**Absolute value Graphs**civicpride-kusatsu.net Topical synopsis | Algebra 2 overview | MathBits" Teacher sources

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We recognize that the absolute worth of a number is always positive (or zero). We deserve to see this same an outcome reflected in the graph of the absolute value parent function 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 Linear "pieces" will appear in the equation the the pure value role in the complying with manner: | 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. |

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