1. Precalculus PreAP/Dual, Revised ©2018 §1.7: Piecewise Functions
Section 1.7
Precalculus PreAP/Dual, Revised ©2018
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§1.7: Piecewise Functions

2. §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.
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§1.7: Piecewise Functions

3. §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.
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§1.7: Piecewise Functions

4. 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
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§1.7: Piecewise Functions

5. §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
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§1.7: Piecewise Functions

6. §1.7: Piecewise Functions
Your Turn
Graph 𝒇 𝒙 = 𝟑𝒙, 𝒊𝒇 𝒙≤𝟎 𝟒, 𝒊𝒇 𝒙>𝟎
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§1.7: Piecewise Functions

7. §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
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§1.7: Piecewise Functions

8. §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
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§1.7: Piecewise Functions

9. §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
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§1.7: Piecewise Functions

10. §1.7: Piecewise Functions
Example 6
Determine the graph of this function.
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§1.7: Piecewise Functions

11. §1.7: Piecewise Functions
Your Turn
Determine the graph of this function.
12/8/2018 8:12 PM
§1.7: Piecewise Functions

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