Writing Recursive Equations for Linear Relationships

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.

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

• 20

• 8

• 3

• 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.

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

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.

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

• 0

• 25

• 5

• 20

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.

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

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.

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.