Lesson 2-2 Extension: Piecewise Functions LO: I can graph piecewise functions by using a table of values. I can
graph absolute value functions using piecewise functions or by using a table of values.
Date: ________________
Piecewise Function – A Function in which different equations are used for
different intervals of the domain. It is defined in pieces.
Absolute Value Function – A piecewise function, written as 𝒇(𝒙)=
|𝒙|, 𝒘𝒉𝒆𝒓𝒆 𝒇(𝒙)≥ 𝟎 𝒇𝒐𝒓 𝒂𝒍𝒍 𝒗𝒂𝒍𝒖𝒆𝒔 𝒐𝒇 𝒙. An absolute value function will always
have a V-Shaped graph. If the coefficient in front of the absolute value symbol is
positive, the v-shape will open upwards. If the coefficient In front of the absolute
value symbol is negative, the v-shape will open downwards.
Consider 𝒇(𝒙)=|𝒙|, this function can be written as a piecewise function:
𝒇(𝒙)= 𝒇(𝒙)={−𝒙, 𝒙 < 𝟎
𝒙, 𝒙 ≥ 𝟎
EX.1 – Graphing Absolute Value Functions
Graph the following absolute value functions using piecewise functions.
a.) 𝒇(𝒙)= 𝟐|𝒙|− 𝟔 b.) 𝒇 = −𝟐|𝒙|+ 𝟑 c.) 𝒇(𝒙)=|𝒙 + 𝟔|
