Week 5: Inverse functions, Implicit functions and Implicit differentiation

Question 1

What is the definition of a function?

Answer 1

A function will have the property that for each x-value (input), there will only be one y-value (output).

Question 2

How do you test for a function?

Answer 2

Using the vertical line test.

If the vertical line only cuts once, then the line is a function.

Question 3

What is a 1-1 Function?

Answer 3

A one to one function has the properties:

• for each x-value (input), there will only be one y-value (output).
• for each y-value there will only be 1 x-value

Question 4

How do you test for a 1-1 function?

Answer 4

To be a 1-1 function, must pass the vertical line test and the horizontal line test.

Question 5

What is the property which creates a 1-1 function?

Answer 5

To be a 1-1 function, a function must always be either increasing or decreasing.