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Name: ____________________________________________ Date: _________________ F.BF Day 1F.BF 1Write a function that describes a relationship between two quantities.1aDetermine an explicit expression and the recursive process (steps for calculation) from context. For example, if Jimmy starts off with $15 and earns $2 a day, the explicit expression “2x+15” can be described recursively (either in writing or verbally) as “to find out how much money Jimmy will have tomorrow, you add $2 to his total today”. J0=15; Jn=Jn-1+2F.BF 2Write arithmetic and geometric sequences recursively and explicitly, use them to model situations and translate between the two forms. Connect arithmetic sequences to linear functions and geometric sequences to exponential functions. x – independent variable and y – dependent variableLinear FunctionsSlope-Intercept formy=mx+bm : Slope b : y-interceptHow you move Where you beginincrease/decrease or start (output of 0)Example 1:An airplane 30,000 feet above the ground begins descending at the rate of 2000 feet per minute. Assume the plane continues at the same rate of descent. The plane’s height and minutes above the ground are related to each other.Independent variable (x): minutes above the grounddependent variable (y): plane’s heightEquation: y = -2000x + 30000Example 2: For the sequence: 4, 7, 10, 13, …The explicit formula is an = 4 + (n – 1)(3)The recursive formula is an = an – 1 +3The function could also be: f(x) = 3x + 1Explicit Form for Arithmetic Sequencesan=a1+n-1dRecursive Form for Arithmetic Sequencesan=an-1+dn : term # a1 : first term d : common differencean : nth term an-1 : previous termExponential FunctionsExponential Equationy=abxb: ratio a : y-interceptWhat you keep Where you beginmultiplying or start (output of 0)Example 1:Jessica has $2000 to invest. The account increases by 5% each year. Write a function to model this situation. Independent variable (x): time in yearsDependent variable (y): total amount in accountEquation: y = 2000(1.05)xExample 2: For the sequence: 9, 3, 1, …The explicit formula is an=913n-1The recursive formula is an=13(an-1)The function could also be: gx=2713xExplicit form for Geometric Sequencesan=a1?rn-1Recursive Form for Geometric Sequencesan=ran-1n : term # a1 : first term r : common ratioan : nth term an-1 : previous termReview items#1 #2#3Sample EOC items#1#2#3#4#5#6#7Which function is modeled in this table?#8Which explicit formula describes the pattern in this table?Writing Quadratic Functions Examples#1#2#3Solutions to Writing Quadratic Equations#1#2#3 ................
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