Using Functions: Understanding the Input-Output Relationship

The video tutorial explains the concept of functions, describing them as special relationships where each input has a single output. It uses the analogy of a function machine to illustrate how inputs are processed to produce outputs. The tutorial covers basic and complex examples, including algebraic notation and substitution, and introduces common functions like trigonometric functions and the area of a circle. The video emphasizes understanding the process of substituting values into functions to obtain outputs.

What is the role of the independent variable in a function?

• It determines the output of the function.

• It is the result of the function.

• It is the same as the dependent variable.

• It is always a constant value.

In a function machine, if the input is 3 and the operations are 'add 6' and 'multiply by 2', what is the output?

• 12

• 18

• 9

• 15

Which of the following is an example of a common function?

• Area of a circle

• Volume of a cube

• Perimeter of a rectangle

• Area of a square

What does the notation F(x) represent in functions?

• The output of the function

• The input variable

• The name of the function

• The constant value in the function

If F(x) = x + 2, what is F(4)?

• 2

• 6

• 4

• 8

How do you determine the output of a function when given an input?

• By guessing the output

• By substituting the input into the function

• By using a calculator

• By looking at a graph

What is the output of G(x) = sqrt(4x - 3) when x = 21?

• 5

• 9

• 7

• 11

In the function F(t) = 3t^2 + 2, what is F(2)?

• 16

• 10

• 12

• 14

Which function output is larger: G(21) or F(2)?

• Both are equal

• F(2)

• Cannot be determined

• G(21)

What is the key process involved in evaluating functions?

• Multiplication

• Addition

• Substitution

• Division