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