One-to-One functions or NOT

Front

What is a One-to-One Function?

Back

A function where each input has a unique output, meaning no two different inputs produce the same output.

Front

What is a NOT One-to-One Function?

Back

A function where at least two different inputs produce the same output.

Front

Example of a One-to-One Function: y = 2x + 3. Is it One-to-One?

Back

Yes, because each x-value corresponds to a unique y-value.

Front

Example of a NOT One-to-One Function: y = x^2. Is it One-to-One?

Back

No, because both x = 2 and x = -2 produce the same y-value (4).

Front

What is the horizontal line test?

Back

A method to determine if a function is one-to-one; if any horizontal line intersects the graph more than once, the function is NOT one-to-one.

Front

Are linear functions always One-to-One?

Back

Yes, as long as they have a non-zero slope.

Front

Are quadratic functions One-to-One?

Back

No, they are NOT One-to-One because they can produce the same output for different inputs.

Front

What is the relationship between One-to-One functions and inverses?

Back

Only One-to-One functions have inverses that are also functions.

Front

If a function is NOT One-to-One, what can be said about its inverse?

Back

The inverse will not be a function.

Front

What is an example of a One-to-One relationship in real life?

Back

Each student assigned to a unique student ID.