Question

Explain in your own words why the horizontal line test determines whether a function is one-to-one.

Name: Problem 18, Chapter 0: Calculus
Uploaded: 2022-02-06T00:57:07-08:00
Duration: 1 min
Channel: Raj Bala
Description: Explain in your own words why the horizontal line test determines whether a function is one-to-one.

   Explain in your own words why the horizontal line test determines whether a function is one-to-one.

Calculus

Laura Taalman, Peter… 1st Edition

Chapter 0, Problem 18

Instant Answer

Solved by Expert Raj Bala

02/06/2022

Step 1

A function $f$ is said to be one-to-one (or injective) if for every $x$ and $y$ in the domain of $f$, $f(x) = f(y)$ implies that $x = y$. In other words, no two different inputs will produce the same output. Show more…

Show all steps

Thanks for your feedback!

Explain in your own words why the horizontal line test determines whether a function is one-to-one.

Play audio

Feedback

Raj Bala and 77 other subject Algebra educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

One-to-One Function

A one-to-one function, also known as an injective function, is one where each output value is produced by exactly one input value. This means that if you pick any two distinct inputs, their outputs are guaranteed to be different, ensuring that there’s a unique pairing between inputs and their resulting outputs.

Horizontal Line Test

The horizontal line test is a graphical method used to determine if a function is one-to-one. By drawing horizontal lines across the graph, you can check whether any line hits the graph more than once. If it does, this indicates that there are multiple inputs that yield the same output, meaning the function is not one-to-one. However, if every horizontal line intersects the graph at most once, the function maintains a one-to-one correspondence.

Please give Ace some feedback