One-to-One & Inverse Functions Practice

Front

What is a function?

Back

A relation where each input has exactly one output.

Front

What is a one-to-one function?

Back

A function where each output is associated with exactly one input.

Front

How can you determine if a relation is a function?

Back

Use the vertical line test: if a vertical line intersects the graph at more than one point, it is not a function.

Front

What is the inverse of a function?

Back

A relation that reverses the input-output pairs of the original function.

Front

How do you find the inverse of a function algebraically?

Back

Replace f(x) with y, swap x and y, and solve for y.

Front

What does reflecting a graph over the line y = x mean?

Back

It means that for every point (a, b) on the graph, there is a corresponding point (b, a) on the reflected graph.

Front

What is the horizontal line test?

Back

A test to determine if a function is one-to-one; if a horizontal line intersects the graph more than once, it is not one-to-one.

Front

What is the significance of the line y = x in relation to functions?

Back

It is the line over which the original function and its inverse are reflections.

Front

Can a function be both one-to-one and onto?

Back

Yes, such a function is called a bijection.

Front

What is an example of a one-to-one function?

Back

f(x) = 2x + 3 is one-to-one because it passes the horizontal line test.