Backtracking and Function Rules

The video tutorial explains how to use backtracking to find input values for functions given an output. It demonstrates this method through various examples, including simple functions, algebraic equations, complex expressions, and a real-world savings problem. The process involves reversing the order of operations and applying inverse operations to solve for the unknown variable.

What is the main goal of backtracking in function rules?

• To find the output value from a given input

• To determine the function rule itself

• To calculate the input value from a known output

• To simplify the function rule

In backtracking, what is the first step when you know the output value?

• Multiply the output by a constant

• Reverse the order of operations

• Add a constant to the output

• Perform the operations in the same order

If a function rule is 'output = 2 * input - 3', what is the input when the output is 9?

• 9

• 6

• 3

• 12

How can you verify your backtracking result?

• By checking the input value against a different rule

• By substituting the input value back into the original rule

• By using a calculator

• By guessing the input value

In the equation y = 4x + 7, what is the value of x when y is 27?

• 4

• 7

• 6

• 5

What is the first operation to reverse in the equation y = 4x + 7 when backtracking?

• Multiply by 4

• Add 7

• Divide by 4

• Subtract 7

In a complex expression, what should you do first when backtracking?

• Simplify the expression

• Guess the input value

• Identify and reverse the last operation

• Perform all operations simultaneously

For the expression (n + 5) * 3 - 6 / 2 = 9, what is the value of n?

• 2

• 3

• 4

• 5

What is the first step in backtracking the expression (n + 5) * 3 - 6 / 2 = 9?

• Add 5

• Multiply by 3

• Subtract 6

• Multiply by 2

In the savings plan example, what are the dependent and independent variables?

• Weeks and money saved

• Interest rate and money saved

• Weeks and interest rate

• Money saved and weeks