Function Invertibility and Tests

The video tutorial explains how to determine if a function has an inverse by using graphical methods. It introduces the vertical and horizontal line tests to identify functions and their invertibility. Examples of different functions, such as lines, parabolas, and cubic functions, are used to illustrate these concepts. The tutorial also defines one-to-one functions, which are functions that have a unique correspondence between x and y values, making them invertible.

What is the primary purpose of determining if a function has an inverse?

• To determine the function's continuity

• To find the function's domain

• To understand the function's range

• To identify if the function can be undone

Which test is used to determine if a graph represents a function?

• Vertical line test

• Horizontal line test

• Diagonal line test

• Slope test

What does the vertical line test check for in a graph?

• If the graph is differentiable

• If the graph is invertible

• If the graph is a function

• If the graph is continuous

Which test is used to determine if a function is invertible?

• Continuity test

• Slope test

• Horizontal line test

• Vertical line test

What does the horizontal line test check for in a function?

• If the function is continuous

• If the function is differentiable

• If the function is a function

• If the function is invertible

What does it mean if a function passes the horizontal line test?

• The function is continuous

• The function is a one-to-one function

• The function is a parabola

• The function is differentiable

What is the significance of the horizontal line test in determining a function's invertibility?

• It checks if the function is continuous

• It checks if the function is a function

• It checks if the function is invertible

• It checks if the function is differentiable

What is the outcome if a function passes both the vertical and horizontal line tests?

• The function is differentiable

• The function is invertible

• The function is continuous

• The function is a parabola

What does the horizontal line test ensure about a function's y-values?

• Each y-value maps to two x-values

• Each y-value maps to multiple x-values

• Each y-value maps to no x-values

• Each y-value maps to exactly one x-value

Why does a parabola fail the horizontal line test?

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

• It is not a function

• It is not continuous

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