Evaluating and Graphing Piecewise Functions: Finding Zeros, Intercepts, and Equations, Study notes of Differential Equations

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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:

Example 4 Writing^ Equations^ of^ Piecewise^ Functions^ Given^ a^ Graph

check using a graphing calculator

On your whiteboard...

Write the equation of the

piecewise graph and check

using a graphing calculator.