Piecewise Functions and Limits

Objectives I can write equations for graphed piecewise functions I can write limits for graph end behavior in Limit Notation

REMEMBER that piece-wise functions are made up of different functions over various domains Copyright © by Houghton Mifflin Company, Inc. All rights reserved.

Piecewise-Defined Functions A piecewise-defined function is composed of two or more functions. f(x) = 3 + x, x < 0 x2 + 1, x 0 Use when the value of x is less than 0. Use when the value of x is greater or equal to 0. x y 4 -4 open circle closed circle (0 is not included.) (0 is included.) Copyright © by Houghton Mifflin Company, Inc. All rights reserved. Piecewise-Defined Functions

Yesterday we graphed these functions. TODAY we will work backwards and write the equations from the graph

FIRST, we need to identify the equation from transformations

Writing Equations from Graphs

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SECOND, we need to identify the Domain Restrictions for each piece

Copyright © by Houghton Mifflin Company, Inc. All rights reserved.

Copyright © by Houghton Mifflin Company, Inc. All rights reserved.

Limits and limit notation. Limits are used to describe the end behavior of a graph. Question: As you substitute x values approaching a set number into to the function, do the f(x) or y values approach a number? That is, does it have a limit?

End Behavior: VERBALLY As x approaches f(x) increases without bound. f(x) decreases without

Limit Notation: also used to show end behavior

End Behavior: LIMIT NOTATION

End Behavior: LIMIT NOTATION

End Behavior: LIMIT NOTATION

Homework WS 1-9 Quiz next class Copyright © by Houghton Mifflin Company, Inc. All rights reserved.