Function Tests: Vertical and Horizontal Line

The video tutorial explains how to determine if a function has an inverse using the horizontal line test. It demonstrates graphically finding the inverse by reflecting the function over the line Y equals X. Examples include a cubic-like function that has an inverse and a quadratic function that does not, due to failing the horizontal line test. The tutorial emphasizes the relationship between the horizontal and vertical line tests in determining invertibility.

What is the purpose of the horizontal line test?

• To find the slope of a function

• To calculate the derivative of a function

• To check if a function is one-to-one

• To determine if a graph is a function

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

• The function is invertible

• The function is one-to-one

• The function is not continuous

• The function is a polynomial

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

• Integrability

• One-to-one nature

• Differentiability

• Continuity

What is the result of a function passing the horizontal line test?

• The function is a polynomial

• The function is invertible

• The function is not continuous

• The function is one-to-one

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

• One-to-one nature

• Differentiability

• Continuity

• Integrability

What is the result of a function passing the horizontal line test?

• The function is one-to-one

• The function is a polynomial

• The function is not continuous

• The function is invertible

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

• Continuity

• Differentiability

• One-to-one nature

• Integrability

Which line is used to reflect a function to find its inverse graphically?

• x = y

• y = x

• x = 0

• y = 0

What happens to the roles of x and y when finding an inverse graphically?

• They are squared

• They remain the same

• They are multiplied by -1

• They are switched

What is the result of reflecting a function over the line y = x?

• The original function

• The inverse of the function

• The integral of the function

• The derivative of the function