Understanding Invertible Functions

The video tutorial explains how to make a non-invertible function invertible by restricting its domain. It introduces the vertical and horizontal line tests to determine function invertibility. The tutorial discusses the mapping of functions and inverse functions, highlighting the importance of one-to-one mapping. It concludes by identifying specific intervals where the function can be restricted to become invertible.

What is the purpose of restricting a function's domain?

• To make it non-invertible

• To make it pass the horizontal line test

• To make it a circle

• To make it pass the vertical line test

What does the vertical line test determine?

• If a function is invertible

• If a function is differentiable

• If a graph represents a function

• If a function is continuous

What does the horizontal line test check for?

• If a function is differentiable

• If a function is invertible

• If a function is continuous

• If a graph represents a function

What happens when you swap x and y values in a function's graph?

• The graph remains unchanged

• The graph becomes a straight line

• The graph becomes a circle

• The graph reflects over the line y = x

Why is it problematic for multiple domain elements to map to the same range element?

• It makes the function non-differentiable

• It makes the inverse not a function

• It makes the function non-continuous

• It makes the function a circle

What is a key requirement for a function to be invertible?

• It must pass the vertical line test

• It must pass the horizontal line test

• It must be a linear function

• It must be a quadratic function

Which interval was identified as invertible in the video?

• 6 to 8

• Negative 2 to 2

• 0 to 4

• Negative 8 to 8

What does the inverse of a function look like when it is invertible?

• A circle

• A straight line

• A parabola

• A reflection over the line y = x

Which test is used to determine if a function's inverse is also a function?

• Derivative test

• Vertical line test

• Horizontal line test

• Slope test

What is the result of restricting the domain of a function to an interval that passes the horizontal line test?

• The function becomes non-continuous

• The function becomes non-differentiable

• The function becomes invertible

• The function becomes a circle