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EvaluatingPiecewiseFunctions
A]
B]
Determinewhichpieceisusedbasedonthedomainrestrictionsgiven.
Substitutexintothatpieceandevaluatefory.
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Evaluating and Graphing Piecewise Functions: Finding Zeros, Intercepts, and Equations, Study notes of Differential Equations
Examples and instructions for determining which piece of a piecewise function to use based on domain restrictions, evaluating the function for given x values, graphing piecewise functions, finding zeros and intercepts, and writing equations for piecewise functions. It includes exercises for practice.
Typology: Study notes
2021/2022
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Example
1 Evaluating Piecewise Functions
A] B]
Determine which piece is used based on the domain restrictions given.
Substitute x into that piece and evaluate for y.
On your whiteboard...
Find:
A]
B]
Find:^ _
= undefined
Talk & Try
In the lab, we cut and pasted pieces of functions together to create the graph.
How can you sketch the graph without scissors and glue?
Sketch on your whiteboard
Example 3 Characteristics of Piecewise Functions
A]
Zero(s):
yint:
To find the yint (0,y): 1] Find the subfunction where x=o works in the subdomain 2] Substitute 0 for x in that subfunction and evaluate To find the zeros (x,0): 1] Set each subfunction equal to zero and solve for x 2] Check the zeros for each subfunction in its subdomain. If it is restricted from the domain, it is extraneous.
Example 3 Characteristics of Piecewise Functions
B]
To find the yint (0,y): 1] Find the subfunction where x=o works in the subdomain 2] Substitute 0 for x in that subfunction and evaluate To find the zeros (x,0): 1] Set each subfunction equal to zero and solve for x 2] Check the zeros for each subfunction in its subdomain. If it is restricted from the domain, it is extraneous. Zero(s): yint: