Precalculus PreAP/Dual, Revised ©2018 §1.7: Piecewise Functions Section 1.7 Precalculus PreAP/Dual, Revised ©2018 viet.dang@humbleisd.net 12/8/2018 8:12 PM §1.7: Piecewise Functions

§1.7: Piecewise Functions Example 1 Given 𝒇 𝒙 = 𝟐𝒙+𝟏 𝒊𝒇 𝒙<𝟒 𝒙 𝟐 +1 𝒊𝒇 𝟒≤𝒙≤𝟏𝟎 , Solve for 𝒇 −𝟓 , 𝒇 𝟖 , and the domain of 𝒇. 12/8/2018 8:12 PM §1.7: Piecewise Functions

§1.7: Piecewise Functions Example 2 Given 𝒈 𝒙 = 𝟐𝒙+𝟏 𝒊𝒇 𝒙>𝟑 𝟕−𝒙 𝒊𝒇 𝒙≤𝟑 , Solve for 𝒈 𝟎 , 𝒈 𝟑 , and the domain of 𝒈. 12/8/2018 8:12 PM §1.7: Piecewise Functions

Graphing Piecewise Functions Piecewise Functions are equations where there is a combination of equations Use a T–CHART for all given equations and plot points. Know the BEGINNING and ENDING points Fill in the t-chart with the appropriate points with at least one or two points beyond the extreme. Overlap the points that associate with open or closed dots Determine the RESTRICTIONS OPEN Dot: Greater or Less than CLOSED Dot: Greater or Less than OR Equal to DARKEN the appropriate graphs 12/8/2018 8:12 PM §1.7: Piecewise Functions

§1.7: Piecewise Functions Example 3 Graph 𝒇 𝒙 = 𝟑𝒙, 𝒊𝒇 𝒙≠𝟎 𝟒, 𝒊𝒇 𝒙=𝟎 𝒙 𝟑𝒙 𝟒 −𝟓 −𝟒 −𝟑 −𝟐 −𝟏 𝟎 𝟏 𝟐 𝟑 𝟓 𝟑𝒙 −𝟏𝟓 −𝟏𝟐 −𝟗 −𝟔 −𝟑 𝑶𝑷𝑬𝑵 𝟑 𝟔 𝟗 𝟏𝟐 𝟏𝟓 𝟒 12/8/2018 8:12 PM §1.7: Piecewise Functions

§1.7: Piecewise Functions Your Turn Graph 𝒇 𝒙 = 𝟑𝒙, 𝒊𝒇 𝒙≤𝟎 𝟒, 𝒊𝒇 𝒙>𝟎 12/8/2018 8:12 PM §1.7: Piecewise Functions

§1.7: Piecewise Functions Example 4 Graph 𝒇 𝒙 = 𝟐𝒙+𝟓, 𝒊𝒇 𝒙<−𝟒 𝟑, 𝒊𝒇 −𝟒≤𝒙≤𝟒 𝟐𝒙−𝟑, 𝒊𝒇 𝒙>𝟒 𝒙 𝟐𝒙+𝟓 𝟑 𝟐𝒙−𝟑 −𝟓 −𝟒 −𝟑 −𝟐 −𝟏 𝟎 𝟏 𝟐 𝟒 𝟓 –5 –3 3 3 3 3 3 3 3 3 3 5 7 12/8/2018 8:12 PM §1.7: Piecewise Functions

§1.7: Piecewise Functions Example 5 Graph 𝒇 𝒙 = |𝒙−𝟏|, 𝒊𝒇 𝒙≤−𝟑 −𝟐, 𝒊𝒇 −𝟑<𝒙<𝟏 𝒙 𝟐 +𝟐, 𝒊𝒇 𝒙≥𝟏 𝒙 |𝒙−𝟏| −𝟐 𝒙 𝟐 +𝟐 −𝟒 −𝟑 −𝟏 𝟎 𝟏 𝟐 5 4 –2 –2 –2 –2 –2 3 6 12/8/2018 8:12 PM §1.7: Piecewise Functions

§1.7: Piecewise Functions Your Turn Graph 𝒇 𝒙 = 𝟑𝒙+𝟖, 𝒊𝒇 𝒙≤−𝟑 −𝟐𝒙, 𝒊𝒇 −𝟑<𝒙<𝟏 𝒙 𝟐 −𝟒, 𝒊𝒇 𝒙≥𝟏 𝒙 𝟑𝒙+𝟖 −𝟐𝒙 𝒙 𝟐 −𝟒 −𝟒 −𝟑 −𝟐 −𝟏 𝟎 𝟏 𝟐 –4 –1 6 4 2 –2 –3 12/8/2018 8:12 PM §1.7: Piecewise Functions

§1.7: Piecewise Functions Example 6 Determine the graph of this function. 12/8/2018 8:12 PM §1.7: Piecewise Functions

§1.7: Piecewise Functions Your Turn Determine the graph of this function. 12/8/2018 8:12 PM §1.7: Piecewise Functions

§1.7: Piecewise Functions Assignment Worksheet 12/8/2018 8:12 PM §1.7: Piecewise Functions