Absolute Value as Piecewise Functions Lesson2.5

Example x + 1, if x < 1 2, if 1 ≤ x ≤ 3 (x-3)2 + 2, if x > 3

Absolute Value as Piecewise We usually write an absolute value function as f (x)= x , but since absolute value is a measure of distance and distance is always positive, it also can be written as follows: -x, if x < 0 x, if x ≥ 0 f (x) =

Writing Abs. Value as Piecewise To identify the number in the domain, set x – h = 0 and solve for x. For I x - h I ≥ 0, simplify the equation given by distributing and combining like terms. For I x - h I < 0, substitute –(x - h) in place of I x - h I. Then, simplify the equation given by distributing and combining like terms.

Example: Write y = 2 Ix – 4I – 10 as a piecewise function. Use 4 in your domain. For (x-4) ≥ 0 2(x – 4) – 10 = 2x – 8 – 10 = 2x – 18 (when x ≥ 4) For (x-4) < 0 2[-(x-4)] – 10 = 2(-x + 4) – 10 = -2x + 8 – 10 = -2x – 2 (when x < 4))

More Examples: Write y = 2 Ix – 4I – 10 as a piecewise function. For (x-4) ≥ 0 2(x – 4) – 10 = 2x – 8 – 10 = 2x – 18 (when x ≥ 4) For (x-4) < 0 2[-(x-4)] – 10 = 2(-x + 4) – 10 = -2x + 8 – 10 = -2x – 2 (when x < 4))

Graphs of Both y=-2x-2 y=2x-18

EOCT Practice A

EOCT Practice C

Writing Abs. Value as Piecewise Using a graph

Writing Abs. Value as Piecewise Try this one...