Section 2.4 library of functions; piecewise defined function
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This document discusses properties of several mathematical functions including the square root, cube root, and absolute value functions. For each function, it notes whether the function is odd or even and describes the x- and y-intercepts. It also provides piecewise definitions and properties of the absolute value function, including its domain and range.
Section 2.4 library of functions; piecewise defined function
- 1. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Section 2.4 Library of Functions; Piecewise-defined Functions
- 2. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
- 3. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. The Square Root Function
- 4. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. ( ) ( )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.
- 5. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. The Cube Root Function
- 6. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. ( ) ( )(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.
- 7. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. The Absolute Value Function
- 8. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
- 9. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
- 10. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
- 11. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
- 12. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
- 13. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
- 14. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
- 15. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
- 16. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. W ISE FUNCTIONS
- 17. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. ( ) ( )(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 ∞