Understanding Recursive Functions

The video tutorial explains how to solve a recurrence relation for a function f, given different initial conditions. It demonstrates the step-by-step process of calculating the values of f(1), f(2), f(3), and f(4) using the recurrence formula f(n+1) = 2*f(n) + 3. The tutorial first uses an initial condition of f(0)=0 and then recalculates using f(0)=3, highlighting the importance of initial conditions in recursive functions.

What is the recurrence formula for the function f?

• f(n+1) = 2f(n) - 3

• f(n+1) = 3f(n) + 2

• f(n+1) = 2f(n) + 3

• f(n+1) = f(n) + 3

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CCSS.8.F.A.1

CCSS.HSF.IF.A.1

Given f(0) = 0, what is the value of f(1)?

• 0

• 1

• 2

• 3

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CCSS.HSF.IF.A.3

How is f(2) calculated using f(1)?

• f(2) = 2f(1) - 3

• f(2) = 3f(1) + 2

• f(2) = 2f(1) + 3

• f(2) = f(1) + 3

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CCSS.8.F.A.1

CCSS.HSF.IF.A.1

What is the value of f(3) if f(2) is 9?

• 21

• 18

• 19

• 20

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CCSS.8.F.A.1

CCSS.HSF.IF.A.1

What is the final value of f(4) when f(0) = 0?

• 45

• 44

• 43

• 42

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CCSS.8.F.A.1

CCSS.HSF.IF.A.1

What is a key drawback of recursive functions as discussed?

• They are difficult to understand.

• They require previous values to compute new ones.

• They are computationally expensive.

• They are not flexible.

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CCSS.8.F.A.1

CCSS.HSF.IF.A.1

What is the new value of f(1) when f(0) is changed to 3?

• 6

• 7

• 8

• 9

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CCSS.8.F.A.1

CCSS.HSF.IF.A.1

If f(1) is 9, what should f(2) be?

• 18

• 19

• 20

• 21

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CCSS.HSF.IF.A.2

What is the value of f(3) when f(2) is 21?

• 45

• 42

• 43

• 44

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CCSS.HSF.IF.A.2

What is the final value of f(4) when f(0) = 3?

• 90

• 91

• 92

• 93

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CCSS.HSF.IF.A.2