Understanding Inverses and Ordered Pairs

Front

What is an ordered pair?

Back

An ordered pair is a pair of elements (x, y) where the first element is the x-coordinate and the second element is the y-coordinate.

Front

What does it mean to find the inverse of an ordered pair?

Back

To find the inverse of an ordered pair (x, y), you switch the positions of x and y to get (y, x).

Front

What is the inverse of the ordered pair (2, 3)?

Back

The inverse of (2, 3) is (3, 2).

Front

How do you find the inverse of a set of ordered pairs?

Back

To find the inverse of a set of ordered pairs, switch the x and y values for each pair.

Front

What is the inverse of the set {(1, 2), (3, 4)}?

Back

The inverse of the set {(1, 2), (3, 4)} is {(2, 1), (4, 3)}.

Front

If a function passes through (a, b), what point does its inverse pass through?

Back

If a function passes through (a, b), its inverse passes through (b, a).

Front

What is the graphical representation of an inverse function?

Back

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

Front

What does it mean for a function to be one-to-one?

Back

A function is one-to-one if each output is produced by exactly one input, meaning no two different inputs map to the same output.

Front

What is the inverse of the function f(x) = 2x + 3?

Back

The inverse of f(x) = 2x + 3 is f^{-1}(x) = (x - 3)/2.

Front

What is the relationship between a function and its inverse?

Back

A function and its inverse undo each other; applying one after the other returns the original input.