What does the graph of a function and it's inverse have in common?

The video tutorial explores the concept of functions and their inverses using Desmos. It discusses the identity function, symmetry about the line y = x, and the characteristics of even and odd functions. The tutorial highlights the relationship between domain and range in functions and their inverses. It also examines examples to illustrate reflections and the importance of domain restrictions when finding inverses. The session concludes with notes on inverse functions and the use of domain restrictions in function studies.

What is the identity function among the basic functions?

• y = sin(x)

• y = x

• y = 1/x

• y = x^2

Which line is often used to test for symmetry in functions and their inverses?

• x = y

• y = x

• x = 0

• y = 0

How are the domain and range of a function and its inverse related?

• They are always equal.

• They are unrelated.

• They are swapped.

• They are identical.

What happens to the domain of a function when finding its inverse?

• It becomes the range of the inverse.

• It remains the same.

• It is doubled.

• It is halved.

What does it mean if a function and its inverse do not reflect over the y = x line?

• The function is linear.

• The function is odd.

• The function is even.

• The inverse is not a function.

What can be done if the inverse of a function is not a function?

• Use a different graph.

• Restrict the domain.

• Change the function.

• Ignore the inverse.

Why might we restrict the domain of a function?

• To simplify calculations.

• To change its range.

• To ensure its inverse is a function.

• To make it more complex.