 ## CCSS.MATH.CONTENT.HSF.IF.C.7.D

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### In this episode of Algebra Applications, students explore various scenarios that can be explained through the use of rational functions. Such disparate phenomena as submarines, photography, and the appearance of certain organisms can be explained through rational function models. This video includes a Video Transcript: https://www.media4math.com/library/video-transcript-algebra-applications-rational-functions ### In spite of their massive size, submarines are precision instruments. A submarine must withstand large amounts of water pressure; otherwise, a serious breach can occur. Rational functions are used to study the relationship between water pressure and volume. Students graph rational functions to study the forces at work with a submarine. This video includes a Video Transcript: https://www.media4math.com/library/video-transcript-algebra-applications-rational-functions-segment-1-submarines A Promethean Flipchart is available for this video: https://www.media4math.com/library/promethean-flipchart-algebra-applications-submarines ### All living things take up a certain amount of space, and therefore have volume. They also have a certain amount of surface area. The ratio of surface area to volume, which is a rational function, reveals important information about the organism. Students look at different graphs of these functions for different organisms. This video includes a Video Transcript: https://www.media4math.com/library/video-transcript-algebra-applications-rational-functions-segment-2-biology A Promethean Flipchart is available for this video: https://www.media4math.com/library/promethean-flipchart-algebra-applications-biology ### The Hubble Telescope has transformed how we view the universe. We learn about the lens formula and how it is used in the construction of telescopes. This video includes a Video Transcript: https://www.media4math.com/library/video-transcript-algebra-applications-rational-functions-segment-3-hubble-telescope A Promethean Flipchart is available for this video: https://www.media4math.com/library/promethean-flipchart-algebra-applications-hubble ### After briefly reviewing the concept of inverse variation, this video explores Boyle’s law, a real world example of an inversely proportional relationship between pressure and volume of a gas. Written and hosted by internationally acclaimed math educator Dr. Monica Neagoy, it goes on to examine similarities and differences among rational functions and numbers. Finally, it takes a look at rational functions graphs and ends with a delightful example merging Euclidean and analytic geometry, thanks to the TI-Nspire technology. Concepts explored: functions, rational expressions, rational functions, asymptotes This video includes a video transcript: https://media4math.com/library/video-transcript-algebra-nspirations-rational-functions-and-expressions A Promethean Flipchart is available for this video: https://www.media4math.com/admin/content?title=promethean&type=library_asset&status=All&langcode=All ### In this Investigation we look at an application of rational functions: Boyle's Law. This video is Segment 1 of a 4 segment series related to Algebra Nspirations: Rational Functions and Expressions. Segments 1 and 2 are grouped together. To access Algebra Nspirations: Rational Functions and Expressions, Segment 2, click the following link: • https://www.media4math.com/library/algebra-nspirations-rational-functions-and-expressions-segment-2 A Video Transcript for Algebra Nspirations: Rational Functions and Expressions, Segments 1 and 2 is available via the following link: • https://www.media4math.com/library/video-transcript-algebra-nspirations-rational-functions-and-expressions-part-1 ### In this Math Lab we explore rational and irrational numbers. This video is Segment 2 of a 4 segment series related to Algebra Nspirations: Rational Functions and Expressions. Segments 1 and 2 are grouped together. To access Algebra Nspirations: Rational Functions and Expressions, Segment 1, click the following link: • https://www.media4math.com/library/algebra-nspirations-rational-functions-and-expressions-segment-1 A Video Transcript for Algebra Nspirations: Rational Functions and Expressions, Segments 1 and 2 is available via the following link: • https://www.media4math.com/library/video-transcript-algebra-nspirations-rational-functions-and-expressions-part-1 ### In this Investigation we look at graphs of rational functions. This video is Segment 3 of a 4 segment series related to Algebra Nspirations: Rational Functions and Expressions. Segments 3 and 4 are grouped together. To access Algebra Nspirations: Rational Functions and Expressions, Segment 4, click the following link: • https://www.media4math.com/library/algebra-nspirations-rational-functions-and-expressions-segment-4 A Video Transcript for Algebra Nspirations: Rational Functions and Expressions, Segments 3 and 4 is available via the following link: • https://www.media4math.com/library/video-transcript-algebra-nspirations-rational-functions-and-expressions-part-2 ### In this Math Lab we look at equivalent rational functions. This video is Segment 4 of a 4 segment series related to Algebra Nspirations: Rational Functions and Expressions. Segments 3 and 4 are grouped together. To access Algebra Nspirations: Rational Functions and Expressions, Segment 3, click the following link: • https://www.media4math.com/library/algebra-nspirations-rational-functions-and-expressions-segment-3 A Video Transcript for Algebra Nspirations: Rational Functions and Expressions, Segments 3 and 4 is available via the following link: • https://www.media4math.com/library/video-transcript-algebra-nspirations-rational-functions-and-expressions-part-2 ### The definition of the term "Graphs of Rational Functions." ### The definition of the term "Rational Functions." ### In this Slide Show, use the Desmos graphing calculator to explore rational functions. Note: The download is a PPT file. ### Algebra Tutorial 1: The graph of a rational function of the form f(x)/g(x), under the following conditions: y = 1/x. ### Algebra Tutorial 2: The graph of a rational function of the form f(x)/g(x), under the following conditions: y = -1/x. ### Algebra Tutorial 3: The graph of a rational function of the form f(x)/g(x), under the following conditions: y = 1/(x + c). ### Algebra Tutorial 5: The graph of a rational function of the form f(x)/g(x), under the following conditions: y = 1/(cx + d). ### Algebra Tutorial 6: The graph of a rational function of the form f(x)/g(x), under the following conditions: y = -1/(cx + d). ### Algebra Tutorial 7: The graph of a rational function of the form f(x)/g(x), under the following conditions: y = 1/(cx - d). ### Algebra Tutorial 8: The graph of a rational function of the form f(x)/g(x), under the following conditions: y = 1/(-cx + d). ### Algebra Tutorial 9: The graph of a rational function of the form f(x)/g(x), under the following conditions: y = (x + a)/(x + b). ### Algebra Tutorial 10: The graph of a rational function of the form f(x)/g(x), under the following conditions: y = (x - a)/(x + b). ### Algebra Tutorial 11: The graph of a rational function of the form f(x)/g(x), under the following conditions: y = (x - a)/(x - b). ### Algebra Tutorial 12: The graph of a rational function of the form f(x)/g(x), under the following conditions: y = (x + a)/[(x + b)(x + c)]. ### Algebra Tutorial 13: The graph of a rational function of the form f(x)/g(x), under the following conditions: y = (x - a)/[(x + b)(x + c)]. ### Algebra Tutorial 14: The graph of a rational function of the form f(x)/g(x), under the following conditions: y = (x + a)/[(x - b)(x + c)]. 