Introduction to Functions

The video introduces the concept of functions as machines that take an input and produce a unique output. It explains the roles of independent and dependent variables, provides examples of simple functions, and discusses real-life applications such as plant growth and speed. The video also covers algebraic representation of functions, including inverse and composite functions, and emphasizes the importance of understanding functions in both mathematical and everyday contexts.

What is the main characteristic of a function in terms of input and output?

• Each input can have multiple outputs.

• Each input has a unique output.

• The output is always greater than the input.

• The input and output are always equal.

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

• It determines the output.

• It is the result of the function.

• It is always a constant.

• It is irrelevant to the function.

In the context of plant growth, what role does sunlight and rainfall play?

• They are the output of the function.

• They are the independent variables.

• They are irrelevant to the function.

• They are the dependent variables.

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

• x + 2

• pi r squared

• sine function

• x divided by y

What does the notation f(x) represent in mathematical terms?

• The input of a function

• The output of a function

• The name of a function

• The inverse of a function

What is an inverse function?

• A function that doubles the input

• A function that reverses the operation of the original function

• A function that squares the input

• A function that adds a constant to the input

In a composite function, what happens to the output of the first function?

• It is multiplied by a constant.

• It becomes the input for the next function.

• It is used to find the inverse.

• It is discarded.