YOUNGSTOWN CITY SCHOOLS



YOUNGSTOWN CITY SCHOOLS

MATH: PRECALCULUS

UNIT 1: GRAPHING RATIONAL FUNCTIONS (3 WEEKS) 2013-14

|Synopsis: This unit will begin with a review of linear, absolute value, piecewise, polynomial irrational, exponential, log, and trig |

|functions. After reviewing these functions, rational functions will be taught in depth. |

STANDARDS

F.IF7d Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. (+) graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.

MATH PRACTICES

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning

LITERACY STANDARDS

L-2 Communicate using correct mathematical terminology

L-7 Research mathematics topics or related problems

L-9 Apply [details of mathematical] readings/use information found in texts to support reasoning, and develop a “works cited document” for research done to solve a problem.

|MOTIVATION |TEACHER NOTES |

|Students will read the article “Why Graphing Is So Important” in the link below and also attached to the unit on | |

|pages 8 & 9, then discuss the article with the class. They will then search for occupations that deal with math and| |

|present them to the class or research how graphs can be used in their potential field and turn in a “works cited | |

|document” showing their sources. (F.IF.7a-e, L-2, L-7, L-9) | |

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|Students establish personal and academic goals for the unit | |

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|Teacher previews the Authentic Assessment so students know what to expect at end of unit. | |

|TEACHING-LEARNING |TEACHER NOTES |

|Vocabulary: | |

|Linear | |

|Slope | |

|x-intercepts | |

|y-intercepts | |

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|Continuous | |

|Vertical shift | |

|Horizontal shift | |

|End behavior | |

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|Maximum | |

|Minimum | |

|Vertex | |

|Piece-wise | |

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|Polynomial | |

|Zeros | |

|Exponential | |

|Period | |

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|Midline | |

|Amplitude | |

|holes | |

|Slant asymptotes | |

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|Horizontal asymptotes | |

|Vertical asymptotes | |

|extrapolate | |

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|Note: Numbers 1 through 10 are review items. You want to keep the graphs fairly simple. | |

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|A pretest on factoring will be given to check students’ skills. If they are weak, use the weak areas for review, | |

|insuring that they are comfortable factoring trinomials, difference of two squares, sum and difference of two cubes, | |

|expressions with common factors and factoring by grouping. (MP.4, MP.8, L-2) | |

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|Review graphing linear functions: f(x) = mx + b – discuss slope, x and y intercepts, and continuity. (F.IF.7a, MP.2, | |

|MP.4, MP.8, L-2) | |

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|3. Review graphing exponential functions: f(x) = ax, examine when a>1 and when 0 ................
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