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Advanced Trig

Types of systems Matrices Function notation. Advanced Trig . Topics Substitution Elimination Cramer’s rule. 1. Solve the system below using substitution. x = -11 + y 7x + 4y = -22. 2. Solve the system using elimination. 9x – 7y = 5 10x + 3y = -16.

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Advanced Trig

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  1. Types of systems • Matrices • Function notation Advanced Trig Topics Substitution Elimination Cramer’s rule

  2. 1. Solve the system below using substitution x = -11 + y 7x + 4y = -22

  3. 2. Solve the system using elimination 9x – 7y = 5 10x + 3y = -16

  4. 3. Find a, b, c and d within the Cramer’s rule set up below, then solve using determinants 5x – 3y = 22 6x – 7y = 41 x =

  5. 4. Inconsistent, dependent, or consistent ? • When solving a system if the solution is 0 = 3 what type of system does that indicate? • A system with infinite solutions is a ____________ system • What type of system gives you are reflexive solution when solving this type algebraically? Such as a solution like 6 = 6.

  6. 5. Use your calculator to find the intersection point(s) of the two functions below, type 2ndcalcintersect. f(x) = 3x – 2 g(x) = +1 Truncate to 3 decimal places. (this means, don’t round) Example: if the solution is x = 3.4678 you write x = 3.467

  7. 6. Solve the following systemfind the value for the variable z. 4w + x + 2y – 3z = -16 -3w + 3x – y + 4z = 20 -w + 2x + 5y + z = -4 5w + 4x + 3y – z = - 10

  8. 7. Function notation If f(x) = x + 3 and g(x) = Find • f(2) • g(f(0)) • f(g(a)) • g(f(x)) • g(4) + f(1)

  9. 8. Solve the systemusing any method

  10. 9. What type of system is this? (use as many words as possible)

  11. 10. Function notation If and Find the following • ) • f(g(x))

  12. 11. Word problem Your overhead costs for your lemonade stand is $500 and it costs you $.08 to make one glass of lemonade. If you sell each glass for $1.75, how many glasses do you have to make to break even?

  13. ANSWERS

  14. 1. ANSWERSolve the system below using substitutionSOLUTION x = -11 + y 7x + 4y = -22 (-6,5)

  15. 2. AnswerSolve the system using elimination 9x – 7y = 5 10x + 3y = -16 (-1, -2)

  16. 3. AnswerFind a, b, c and d within the Cramer’s rule set up below, then solve using determinants 5x – 3y = 22 6x – 7y = 41 a = 22 b = 41 c = -3 d = -7 x = =

  17. 4. AnswerInconsistent, dependent, or consistent • When solving a system if the solution is 0 = 3 what type of system does that indicate? parallel • A system with infinite solutions is a ____________ system coinciding • What type of system gives you are reflexive solution when solving this type algebraically? Such as a solution like 6 = 6. coinciding

  18. 5. Answer Use your calculator to find the intersection point(s) of the two functions below f(x) = 3x – 2 g(x) = +1 (-1.302, -5.908) and (2.302, 4.908) (2nd trace)

  19. 6. Solve the following systemfind the value for the variable z. SOLUTION 4w + x + 2y – 3z = -16 -3w + 3x – y + 4z = 20 -w + 2x + 5y + z = -4 5w + 4x + 3y – z = - 10 Steps: enter the matrix into the calculator, then run rref under matrix, math menu. (-1, 1, -2, 3) so z = 3.

  20. 7. Function notationSOLUTIONS If f(x) = x + 3 and g(x) = Find • f(2)= 2 + 3 = 5 • g(f(0))= g(3)=9 – 3 + 1 = 7 • f(g(a))= ( • g(f(x))= • g(4) + f(1)= 13 + 4 = 17

  21. 8. Answer Solve the system using any method • X = -7 • Y = -2

  22. 9. Answer What type of system is this? (use as many words as possible) • parallel

  23. 10. Answers Function notation If and Find the following • = 4 – 6 + 2 = 0 • ) = f(4(0)) = f(0) = 0 – 0 + 2 = 2 • = g(( • = g(4) = 4 x 4 = 16 • f(g(x)) =

  24. 11. Answer Word problem Your overhead costs for your lemonade stand is $500 and it costs you $.08 to make one glass of lemonade. If you sell each glass for $1.75, how many glasses do you have to make to break even? 500 + .08x = 1.75x 500 = 1.67x 299.40 = x you have sell about 300.

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