Lesson7-3:SquareRootFunctionsandInequalities
PastTarget
PresentTarget
FutureTarget
Icansimplifyexpressionswith
Iwillgraphandanalyzesquare
Iwilldeterminethesolutionsof
squareroots.
rootfunctions.
squarerootequationsusing
Iwillgraphsquareroot
algebraicmethods.
inequalities.
Asquarerootfunctionisafunctionthatcontainsthesquarerootofavariable.Itisatypeofradicalfunction.
ParentFunction:𝑓 𝑥 = 𝑥
The______________islimitedtovaluesforwhichthe
𝑥 𝑓(𝑥) radicandisnonnegative,becausewecannot
evaluatethesquarerootofanegativenumber.
The_______________islimitedbytheleastvalueforthe
domain.
TRANSFORMATIONS:
𝑓 𝑥 = 𝑎 𝑥 − ℎ + 𝑘
h
k
a
Ex1:Identifythedomainandrangeof𝑓 𝑥 = 𝑥 − 4.
Domain:Sincetheradicandcannotbenegative, Range:Findthelowerlimitoftherange
set𝑥 − 4 ≥ 0,andsolve. bysubstitutingthelowerlimitofthe
domainintothefunction.
Ex2:Grapheachfunction.Statethedomainandrange.
a.𝑦 = 𝑥 − 2 + 1 b.𝑦 = −2 𝑥 + 3
Ex3:Grapheachsquarerootinequality.
a.𝑦 < 4𝑥 b.𝑦 ≥ 𝑥 + 2
Practice:Grapheachsquarerootfunctionorinequality.For#1-6,statethedomainandrange.