Explicit and Recursive Functions

The video tutorial explains how to derive explicit and recursive equations from a table of values. It starts by introducing the concept of linear functions and demonstrates how to write explicit equations using the y = mx + b formula. The tutorial then shifts focus to recursive functions, explaining how they alter outputs instead of inputs and the importance of defining a starting point.

What are the two types of equations that can be derived from a table of values?

• Polynomial and rational equations

• Explicit and recursive equations

• Exponential and logarithmic equations

• Linear and quadratic equations

What pattern is observed in the outputs 10, 13, 16, 19, and 22?

• Each output is divided by 2

• Each output is added by 3

• Each output is subtracted by 1

• Each output is multiplied by 2

Which of the following is true about linear functions?

• They do not have a y-intercept

• They are always quadratic

• They have a variable rate of change

• They have a constant rate of change

What is the formula for the explicit equation derived from the table?

• y = 3x + 7

• y = 4x + 6

• y = 2x + 5

• y = x + 10

Which of the following is NOT a characteristic of explicit functions?

• They use inputs to calculate outputs

• They require a starting point

• They can be represented by y = mx + b

• They involve arithmetic operations on inputs

What is the output when the input is 3 in the explicit function derived?

• 16

• 19

• 22

• 13

What is the role of the constant in the explicit equation y = 3x + 7?

• It changes the x-values

• It shifts the line vertically

• It alters the y-values

• It determines the slope of the line

What is the y-intercept in the explicit equation y = 3x + 7?

• 3

• 0

• 10

• 7

How do recursive functions differ from explicit functions?

• Recursive functions use inputs to determine outputs

• Recursive functions use outputs to determine the next output

• Recursive functions are always quadratic

• Recursive functions do not require a starting point

In a recursive function, what is the relationship between f(n) and f(n-1)?

• f(n) = f(n-1) / 3

• f(n) = f(n-1) * 3

• f(n) = f(n-1) + 3

• f(n) = f(n-1) - 3