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Introduction to Function

ALGEBRA 1. Introduction to Function. Irma Crespo & Larisa Yezersky. ALGEBRA 1. The Pascal Triangle. Input =1 st diagonal column number Output = number in the diagonal column. Crespo 2009. ALGEBRA 1. The Pascal Triangle. Input = diagonal column number.

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Introduction to Function

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  1. ALGEBRA 1 Introduction to Function Irma Crespo & Larisa Yezersky

  2. ALGEBRA 1 The Pascal Triangle Input =1st diagonal column number Output = number in the diagonal column Crespo 2009

  3. ALGEBRA 1 The Pascal Triangle Input = diagonal column number Output = sum of the numbers in the diagonal column Crespo 2009

  4. A functionis a rule that establishes a relationship between two quantities, called the input and the output. ALGEBRA 1 Function Rules to Live By Input Output 0 1 2 3 4 5 3 1 2 3 4 8 • For each input, there is exactly one output. • There can be more than one input for the same output. • - Larson et.al. Algebra 1. 2001. McDougall Littell Crespo 2009

  5. The domain is the collection of all input values of the independent variable that determines the value of other variables. ALGEBRA 1 Function Rules to Live ByDomain Domain Input Independent Variable x-axis values Crespo 2009

  6. The range is the collection of all output values of the dependent variable whose value is determined by the independent variable. ALGEBRA 1 Function Rules to Live ByRange Range Output Dependent Variable y-axis values Crespo 2009

  7. THE WORD PROBLEM A cell phone company charges $80 for a phone. Its minutes for talk time are charged at a rate of $0.50 per minute up to 300 minutes. The total cost c of the phone and the number of minutes m is given by the function:  c = $80 + $0.50m   If you maximized the talk time minutes, how much could have your parents paid? ALGEBRA 1 Function Junction Crespo 2009

  8. Make a list of inputs (m), use the function to calculate an output (c) and use the rule: 60 ≤ m ≤ 300 to fill in 5 values at most for each input, function, and output columns. ALGEBRA 1 Make the ConnectionList c = 110 c = $80 + $0.50 (60) c = 140 c = $80 + $0.50 (120) c = 170 c = $80 + $0.50 (180) c = 200 c = $80 + $0.50 (240) c = 230 c = $80 + $0.50 (300) Crespo 2009

  9. Record the values into an input/output table. ALGEBRA 1 Make the ConnectionTable Crespo 2009

  10. 60 120 180 240 300 ALGEBRA 1 Make the ConnectionGraph Cost per Minute of Cell Phone Use costs (c) in dollars time in minutes (m) Crespo 2009

  11. The domain of the function is all values of m such that 60 ≤ m ≤ 300 which are: ALGEBRA 1 Make the ConnectionDomain and Range • The range of the function is all values of c as shown above. Crespo 2009

  12. What do the domain and range mean in the problem? ALGEBRA 1 Make the ConnectionYour Interpretation Crespo 2009

  13. Off to the whiteboard for a brief revisit. ALGEBRA 1 Quick Run Crespo 2009

  14. The student government in Pratts High School is facing a dilemma on fundraising. It has to unlock the answers to the Tangram Puzzle in order to fulfill all the school improvement projects for the school year that require $5,000 in the student government treasury. Currently, it only has $1,500 in the coffer. It profits $500 per fundraiser. Represent the number of fundraising events with E and the money gained for the treasury with T. ALGEBRA 1 Practice the Function Crespo 2009

  15. 1.3 Illustrate the algebraic model. 1.2 Indicate the labels 1. Scramble for the function by creating an equation 1.1. Show the verbal model. 2. Create an input/output table for the equation. 3. Represent the table with a labeled line graph. 4. How many fundraising events will it take to reach its target? ALGEBRA 1 Complete the Tangram Crespo 2009

  16. ALGEBRA 1 Tangram Solutions Money gained for the treasury is equal to the money in the treasury at the beginning plus the profits from a fundraiser times the number of fundraising events. number of fundraising events = E money in the treasury at the beginning = $1,500 profits from a fundraiser = $500 money gained for the treasury = T T = $1,500 + 500E where $1,500 < T≤ $5,000 Crespo 2009

  17. ALGEBRA 1 Tangram Solutions Money in the Treasury Per Fundraising Event Money in the Treasury (T) in $ Number of Fundraising Events (E) The student government needs 7 fundraising events to reach its target. Crespo 2009

  18. ALGEBRA 1 What’s Behind the Tangram? Crespo 2009

  19. ALGEBRA 1 What’s Behind the Tangram? Crespo 2009

  20. ALGEBRA 1 The MatchingTime for Fun!!! Crespo 2009

  21. Function Output Input ALGEBRA 1 Exit Slip What did you learn? Crespo 2009

  22. Larson, R.,Boswell L., Kanold, T., & Stiff, L. (2001). Algebra 1. Illinois: McDougall Littell. Microsoft Office for cliparts and base template. PowerPoint created by I.S.Z.B.Crespo. List, tables, graphs, equations, word problems, tangram puzzle, and worksheets are original creations. Lesson plan strictly made by Irma Crespo. ALGEBRA 1 Acknowledgement Crespo 2009

  23. A Lesson Plan Presentation By Irma Crespo & Larisa Yezersky ALGEBRA 1 Thank you! Crespo, Yezersky

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