Overview of one to one functions

The video tutorial explains the concept of functions, focusing on one-to-one functions where each element in the domain maps to a unique element in the range. It uses mapping tools and graphical analysis to illustrate these concepts, highlighting the differences between general functions and one-to-one functions. The tutorial also discusses why parabolas are not one-to-one and the significance of one-to-one functions in understanding inverses.

What is a basic requirement for a function regarding its domain and range?

• Each domain element can map to multiple range elements.

• Each range element must map to a unique domain element.

• Each domain element must map to a unique range element.

• Each range element must map to multiple domain elements.

In a one-to-one function, what is true about the mapping of domain elements?

• Each domain element can map to multiple range elements.

• Each range element must map to multiple domain elements.

• Multiple domain elements can map to the same range element.

• Each domain element must map to a unique range element.

Why is a parabola not considered a one-to-one function?

• It has multiple y-values for a single x-value.

• It has the same y-value for different x-values.

• It does not have any x-values.

• It is a straight line.

What is the significance of one-to-one functions in relation to inverses?

• The inverse of a one-to-one function is always a function.

• The inverse of a one-to-one function is not a function.

• One-to-one functions do not have inverses.

• Inverses are only defined for non-one-to-one functions.

Which graph represents a one-to-one function?

• A hyperbola

• A straight line

• A circle

• A parabola