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Section 3.4 Library of Functions; Piecewise-defined Functions Copyright © 2013 Pearson Education,...

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Section 3.4 Library of Functions; Piecewise-defined Functions Copyright © 2013 Pearson Education, Inc. All rights reserved
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Page 1: Section 3.4 Library of Functions; Piecewise-defined Functions Copyright © 2013 Pearson Education, Inc. All rights reserved.

Section 3.4

Library of Functions;

Piecewise-defined Functions

Copyright © 2013 Pearson Education, Inc. All rights reserved

Page 2: Section 3.4 Library of Functions; Piecewise-defined Functions Copyright © 2013 Pearson Education, Inc. All rights reserved.

Copyright © 2013 Pearson Education, Inc. All rights reserved

Page 3: Section 3.4 Library of Functions; Piecewise-defined Functions Copyright © 2013 Pearson Education, Inc. All rights reserved.

The Square Root Function

Copyright © 2013 Pearson Education, Inc. All rights reserved

Page 4: Section 3.4 Library of Functions; Piecewise-defined Functions Copyright © 2013 Pearson Education, Inc. All rights reserved.

3 3(a) f x x x f x This means the function is odd and symmetric with respect to the origin.

3(b) 0 0 0f x and y intercepts are both 0.

Copyright © 2013 Pearson Education, Inc. All rights reserved

Page 5: Section 3.4 Library of Functions; Piecewise-defined Functions Copyright © 2013 Pearson Education, Inc. All rights reserved.

The Cube Root Function

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Page 6: Section 3.4 Library of Functions; Piecewise-defined Functions Copyright © 2013 Pearson Education, Inc. All rights reserved.

(a) f x x x f x This means the function is even and symmetric with respect to the y-axis.

(b) 0 0 0f x and y intercepts are both 0.

Copyright © 2013 Pearson Education, Inc. All rights reserved

Page 7: Section 3.4 Library of Functions; Piecewise-defined Functions Copyright © 2013 Pearson Education, Inc. All rights reserved.

The Absolute Value Function

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Page 8: Section 3.4 Library of Functions; Piecewise-defined Functions Copyright © 2013 Pearson Education, Inc. All rights reserved.

Copyright © 2013 Pearson Education, Inc. All rights reserved

Page 9: Section 3.4 Library of Functions; Piecewise-defined Functions Copyright © 2013 Pearson Education, Inc. All rights reserved.

Copyright © 2013 Pearson Education, Inc. All rights reserved

Page 10: Section 3.4 Library of Functions; Piecewise-defined Functions Copyright © 2013 Pearson Education, Inc. All rights reserved.

Copyright © 2013 Pearson Education, Inc. All rights reserved

Page 11: Section 3.4 Library of Functions; Piecewise-defined Functions Copyright © 2013 Pearson Education, Inc. All rights reserved.

Copyright © 2013 Pearson Education, Inc. All rights reserved

Page 12: Section 3.4 Library of Functions; Piecewise-defined Functions Copyright © 2013 Pearson Education, Inc. All rights reserved.

Copyright © 2013 Pearson Education, Inc. All rights reserved

Page 13: Section 3.4 Library of Functions; Piecewise-defined Functions Copyright © 2013 Pearson Education, Inc. All rights reserved.

Copyright © 2013 Pearson Education, Inc. All rights reserved

Page 14: Section 3.4 Library of Functions; Piecewise-defined Functions Copyright © 2013 Pearson Education, Inc. All rights reserved.

Copyright © 2013 Pearson Education, Inc. All rights reserved

Page 15: Section 3.4 Library of Functions; Piecewise-defined Functions Copyright © 2013 Pearson Education, Inc. All rights reserved.

Copyright © 2013 Pearson Education, Inc. All rights reserved

Page 16: Section 3.4 Library of Functions; Piecewise-defined Functions Copyright © 2013 Pearson Education, Inc. All rights reserved.

Copyright © 2013 Pearson Education, Inc. All rights reserved

Page 17: Section 3.4 Library of Functions; Piecewise-defined Functions Copyright © 2013 Pearson Education, Inc. All rights reserved.

Copyright © 2013 Pearson Education, Inc. All rights reserved

Page 18: Section 3.4 Library of Functions; Piecewise-defined Functions Copyright © 2013 Pearson Education, Inc. All rights reserved.

WISE

FUNCTIONS

Copyright © 2013 Pearson Education, Inc. All rights reserved

Page 19: Section 3.4 Library of Functions; Piecewise-defined Functions Copyright © 2013 Pearson Education, Inc. All rights reserved.

(a) 0 0 1 1f 1 2f 2 2 (2) 4f

(b) The domain of is [ 1, )f

(d) The range of is (0, )f Copyright © 2013 Pearson Education, Inc. All rights reserved

Page 20: Section 3.4 Library of Functions; Piecewise-defined Functions Copyright © 2013 Pearson Education, Inc. All rights reserved.

(a)

(b)

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Page 21: Section 3.4 Library of Functions; Piecewise-defined Functions Copyright © 2013 Pearson Education, Inc. All rights reserved.

Copyright © 2013 Pearson Education, Inc. All rights reserved

Page 22: Section 3.4 Library of Functions; Piecewise-defined Functions Copyright © 2013 Pearson Education, Inc. All rights reserved.

Copyright © 2013 Pearson Education, Inc. All rights reserved


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