This document provides an introduction to different types of functions including linear, power, absolute value, square root, exponential, rational, and logarithmic functions. For each function, it describes the parent function, domain and range, graph, and examples of real-life uses. The document aims to familiarize the reader with common families of functions and their characteristics and applications.

1. Introduction to Family of Functions

2. Linear Functions Parent Function 𝑓𝑥=𝑥 Domain All Real Numbers Range All Real Numbers

3. Linear Functions Graph

4. Linear Functions Real Life Uses Distance vs. Time Slope (pitch) of a Roof Equal Weekly Deposits Leo Reynolds, Roofline, October 24, 2006 via Flickr, Creative Commons Attribution, Noncommercial & Share Alike

5. Power Functions Parent Function 𝑓𝑥= 𝑥2 𝑎𝑛𝑑 𝑓𝑥= 𝑥3 Domain All Real Numbers Range All Real Numbers

6. Power Functions Graph 𝑓𝑥=𝑥2 𝑓𝑥=𝑥3

7. Power Functions Real Life Uses Falling Objects Volume Area Microsoft Clip Art

8. Absolute Value Functions Parent Function 𝑓𝑥= 𝑥 Domain All Real Numbers Range All PositiveReal Numbers

9. Absolute Value Functions Graph

10. Absolute Value Functions Real Life Uses Currency Exchange Real Time vs. Distance EpSos.de, International Money Pile in Cash and Coins, January 14, 2011 via Flickr, Creative Commons Attribution

11. Square Root Function Parent Function 𝑓𝑥= 𝑥 Domain All Positive Real Numbers Range All Positive Real Numbers

12. Square Root Function Graph

13. Square Root Function Real Life Uses Fly Ball from Behind Home Plate Power Factor Electrical Load Microsoft Clip Art

14. Exponential Functions Parent Function 𝑓𝑥= 2𝑥 Domain All Real Numbers Range All Positive Real Numbers

15. Exponential Functions Graph

16. Exponential Functions Real Life Uses Compound Interest Radioactive Decay Images_of_Money, Piggy Bank with Euro Notes, June 18, 2011 via Flickr, Creative Commons Attribution

17. Rational Functions Parent Function 𝑓𝑥= 1𝑥 Domain All Real Numbers such that the denominator does NOT equal zero Range All Real Numbers

18. Rational Functions Graph

19. Rational Functions Real Life Uses Lighthouse Beam Pressure of a Compressed Gas Thew.g, Tanks, August 4, 2007 via Flickr, Creative Commons Attribution, Noncommercial & Share Alike

20. Logarithmic Functions Parent Function 𝑓𝑥=log𝑥 Domain All Positive Real Numbers Range All Real Numbers

21. Logarithmic Functions Graph

22. Logarithmic Functions Real Life Uses Richter Scale Measurement of Sound Instructional Resources Corporation, Seismograph, 2005 via Discovery Education

23. References Discovery Education. (2005).A seismograph, which records earthquakes. [Image]. Available from http://www.discoveryeducation.com/ epSos.de. (Photographer). (2011). Money piles in cash. [Web]. Retrieved from http://www.flickr.com/photos/epsos/5394616925/ Holt. (n.d.). Online graphing calculator. Retrieved from http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html Images of Money. (Photographer). (2011). Piggy bank with euro notes. [Web]. Retrieved from http://www.flickr.com/photos/59937401@N07/5857148161 Reynolds, L. (Photographer). (2006). Roofline. [Web]. Retrieved from http://www.flickr.com/photos/lwr/278430898/ Thew, G. (Photographer). (2007). Tanks. [Web]. Retrieved from http://www.flickr.com/photos/sophmattgunner/1069308265/