Lesson#12PiecewiseFunctions

Apiecewisefunctionisafunctionthatisacombinationofoneormorefunctions.

Ø Theruleforapiecewisefunctionisdifferentfordifferentparts,orpieces,ofthedomain.

Apiecewisefunctionthatisconstantforeachintervalofitsdomainiscalledastepfunction.Example#1:Graph

𝑦 =−2, 𝑤ℎ𝑒𝑛 𝑥 < 0 1, 𝑤ℎ𝑒𝑛 0 ≤ 𝑥 ≤ 2 5, 𝑤ℎ𝑒𝑛 𝑥 > 2

Toevaluateanypiecewisefunctionforaspecificx-value:1. Findtheintervalofthedomainthatcontainsthatinput2. Usetheruleforthatinterval.

Example#2:EvaluatethePiecewisefunctionforx=-1andx=4.

Lesson#12Example#3:EvaluatethePiecewiseFunctionforx=-2andx=0

Nowlet’sgraphg(x).Example#4:Graphthefunction.

𝑔 𝑥 = (𝑥 − 1)! − 3, 𝑤ℎ𝑒𝑛 𝑥 ≤ 12𝑥 + 3, 𝑤ℎ𝑒𝑛 𝑥 > 1

Lesson#12YouTry:Graphthefunction.

Recall:Anyabsolutevaluefunctioncanberewrittenasapiece-wisefunction.Example#5:Rewritethefunctioninpiecewisenotation.

ℎ 𝑥 = 7 − 𝑥 + 3

Lesson#12Example#6:Rewritethefunctionwithoutanyabsolutevaluenotation.

𝑔 𝑥 = 𝑥 + 3 + 2𝑥 − 1 YouTry:Rewritethefunctioninpiecewisenotation,thengraph.

ℎ 𝑥 = 𝑥 + 3𝑥 − 9

𝑔(𝑥) = |𝑥 + 4| + |𝑥 − 2|