Piecewise-defined Functions

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Piecewise-defined Functions Dr. Fowler  AFM  Unit 1-4 Library of Functions; Piecewise-defined Functions

The Square Root Function Copyright © 2013 Pearson Education, Inc. All rights reserved

The Cube Root Function Copyright © 2013 Pearson Education, Inc. All rights reserved

x and y intercepts are both 0. This means the function is odd and symmetric with respect to the origin. x and y intercepts are both 0. Copyright © 2013 Pearson Education, Inc. All rights reserved

The Absolute Value Function Copyright © 2013 Pearson Education, Inc. All rights reserved

x and y intercepts are both 0. This means the function is even and symmetric with respect to the y-axis. x and y intercepts are both 0. Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Piecewise Functions – “Function in Pieces” https://www. youtube

Evaluating Piecewise Functions “a Function in Pieces” Piecewise functions are functions defined by at least two equations, each of which applies to a different part of the domain A piecewise function looks like this: f(x) = x2 + 1 , x  0 x – 1 , x  0 Domain restrictions Equations

f(x) = Evaluating Piecewise Functions: Evaluating piecewise functions is just like evaluating functions that you are already familiar with. Let’s calculate f(2). f(x) = x2 + 1 , x  0 x – 1 , x  0 You are being asked to find y when x = 2. Domain Restrictions - Since 2 is  0, you will only substitute into the second part of the function. f(2) = 2 – 1 = 1

f(x) = Let’s calculate f(-2). x2 + 1 , x  0 x – 1 , x  0 You are being asked to find y when x = -2. Since -2 is  0, you will only substitute into the first part of the function. f(-2) = (-2)2 + 1 = 5

Try this example: Evaluate each piecewise function for x = –1 and x = 3. 3x2 + 1 if x < 0 g(x) = 5x – 2 if x ≥ 0 Because –1 < 0, use the rule for x < 0. g(–1) = 3(–1)2 + 1 = 4 Because 3 ≥ 0, use the rule for x ≥ 0. g(3) = 5(3) – 2 = 13

 f(x) = Graphing Piecewise Functions: x2 + 1 , x  0 x – 1 , x  0 Determine the shapes of the graphs. Parabola and Line Determine the boundaries of each graph.       Graph the line where x is greater than or equal to zero. Graph the parabola where x is less than zero. 

  f(x) = Graphing Piecewise Functions: 3x + 2, x  -2 Determine the shapes of the graphs. Line, Line, Parabola Determine the boundaries of each graph.          

Excellent Job !!! Well Done