Graphing Inverse Functions

Front

What is an inverse function?

Back

An inverse function reverses the operation of the original function. If f(x) takes an input x and produces an output y, then the inverse function f^-1(y) takes y back to x.

Front

How do you find the inverse of a function algebraically?

Back

To find the inverse of a function, replace f(x) with y, swap x and y, and then solve for y. The resulting equation is the inverse function.

Front

What is the line of symmetry for a function and its inverse?

Back

The line of symmetry for a function and its inverse is the line y = x. This line represents where the function and its inverse are equal.

Front

What does it mean for two functions to be inverses of each other?

Back

Two functions are inverses of each other if applying one function to an input and then applying the other function to the result returns the original input.

Front

How can you verify if two functions are inverses?

Back

To verify if two functions f(x) and g(x) are inverses, check if f(g(x)) = x and g(f(x)) = x for all x in the domain.

Front

What is the inverse of the function f(x) = -3x + 3?

Back

The inverse of the function f(x) = -3x + 3 is f^-1(x) = -1/3x + 1.

Front

What is the significance of the domain and range when finding inverses?

Back

The domain of the original function becomes the range of the inverse function, and the range of the original function becomes the domain of the inverse function.

Front

What is a one-to-one function?

Back

A one-to-one function is a function where each output is produced by exactly one input, ensuring that the inverse function exists.

Front

What is the graphical representation of an inverse function?

Back

The graphical representation of an inverse function is a reflection of the original function across the line y = x.

Front

What is the process to graph the inverse of a function?

Back

To graph the inverse of a function, first graph the original function, then reflect it across the line y = x.