Understanding Functions

The video tutorial explains the concept of functions, specifically focusing on whether y is a function of x. It outlines the criteria for a function, emphasizing that each input x must map to exactly one output y. The tutorial provides examples to illustrate when a relationship is not a function, such as when an input maps to multiple outputs. A table is analyzed to demonstrate these principles, showing that if an input can result in different outputs, it is not a function.

What is a necessary condition for y to be a function of x?

• Each y must map to exactly one x value.

• Each x must map to multiple y values.

• Each x must map to exactly one y value.

• Each y must map to multiple x values.

If a relationship allows multiple y values for a single x, what can we conclude?

• It is a quadratic function.

• It is a function.

• It is a linear function.

• It is not a function.

What happens if a function box outputs more than one y for a given x?

• It becomes a non-function.

• It remains a function.

• It becomes a linear function.

• It becomes a quadratic function.

In the given example, what happens when x equals 1?

• y is undefined.

• y can be either 1 or 2.

• y is always 2.

• y is always 1.

Why is the relationship in the example not a function?

• Because x maps to a single y.

• Because x maps to multiple y values.

• Because y maps to multiple x values.

• Because y maps to a single x.

What must a function do for each input value?

• Map to a variable number of outputs.

• Map to multiple outputs.

• Map to exactly one output.

• Map to no outputs.