The video tutorial explains how to write recursive equations for linear relationships. It begins with an introduction to recursive equations, which use previous values to determine a pattern. The first example demonstrates an increasing pattern where each value is the previous value plus three. The second example shows a decreasing pattern where each value is the previous value minus five. The video concludes with encouragement to engage with the content and apply the concepts learned.

What is a recursive equation?

• An equation that defines a sequence based on a constant value.

• An equation that defines a sequence based on the next term.

• An equation that defines a sequence based on random values.

• An equation that defines a sequence based on the previous term.

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CCSS.HSF.BF.A.2

In the first example, what is the initial value of f(x) when x is 0?

• 20

• 8

• 3

• 5

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CCSS.HSF.LE.B.5

How does f(x) change in the first example?

• It decreases by 3 each time.

• It increases by 5 each time.

• It increases by 3 each time.

• It remains constant.

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2

What is the recursive equation for the first example?

• f(0) = 8, f(x) = f(x-1) - 3

• f(0) = 8, f(x) = f(x-1) + 3

• f(0) = 3, f(x) = f(x-1) - 8

• f(0) = 3, f(x) = f(x-1) + 8

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CCSS.HSF.IF.A.3

What is the pattern in the first example?

• Starts at 8 and decreases by 3 each time.

• Starts at 8 and increases by 3 each time.

• Starts at 25 and decreases by 5 each time.

• Starts at 25 and increases by 5 each time.

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CCSS.HSF.BF.A.2

In the second example, what is the initial value of f(x) when x is 0?

• 0

• 25

• 5

• 20

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CCSS.HSF.LE.B.5

How does f(x) change in the second example?

• It increases by 5 each time.

• It decreases by 3 each time.

• It remains constant.

• It decreases by 5 each time.

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2

What is the recursive equation for the second example?

• f(0) = 25, f(x) = f(x-1) + 5

• f(0) = 25, f(x) = f(x-1) - 5

• f(0) = 5, f(x) = f(x-1) - 25

• f(0) = 5, f(x) = f(x-1) + 25

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CCSS.HSF.IF.A.3

What is the pattern in the second example?

• Starts at 25 and decreases by 5 each time.

• Starts at 8 and increases by 3 each time.

• Starts at 25 and increases by 5 each time.

• Starts at 8 and decreases by 3 each time.

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CCSS.HSF.BF.A.2

What does a recursive equation for a linear relationship typically involve?

• Adding or subtracting a constant value to the previous term.

• Multiplying the previous term by a constant value.

• Dividing the previous term by a constant value.

• Using random values for each term.

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CCSS.HSF.IF.A.3