Converting Geometric Sequences: From Explicit to Recursive Formulas

The video tutorial introduces the function g(x) = 9 * 8^(x-1) defined for positive integers. It explains how to write a recursive definition for this function, starting with a base case and then defining the recursive step. The tutorial includes examples to verify the recursive definition, demonstrating that each term is 8 times the preceding term, starting from 9 when x equals 1.

What is the domain of the function g(x)?

• Negative integers

• All integers

• Positive integers

• All real numbers

What is the value of g(1) according to the function definition?

• 1

• 72

• 9

• 8

What is the value of g(2) according to the function definition?

• 72

• 81

• 64

• 9

What pattern is observed in the function's outputs?

• Each term is 7 times the previous term

• Each term is 8 times the previous term

• Each term is 6 times the previous term

• Each term is 9 times the previous term

What is the base case for the recursive function?

• g(x) = 72 if x = 1

• g(x) = 1 if x = 1

• g(x) = 9 if x = 1

• g(x) = 8 if x = 1

How is g(x) defined for x > 1 in the recursive function?

• g(x) = g(x-1) - 8

• g(x) = g(x-1) / 8

• g(x) = g(x-1) + 8

• g(x) = g(x-1) * 8

What is the value of g(3) using the recursive definition?

• 576

• 72

• 512

• 9

What is the value of g(4) using the recursive definition?

• 9

• 72

• 576

• 512

Why is the function definition considered recursive?

• It refers to itself in its own definition

• It uses a loop

• It is defined for positive integers

• It has a base case

What is the purpose of verifying the recursive function?

• To check if it matches the explicitly defined function

• To find errors in the function

• To simplify the function

• To change the base case