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Numerade Educator

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Problem 1 Medium Difficulty

(a) What is a one-to-one function?
(b) How can you tell from the graph of a function whether it is one-to-one?

Answer

(a) See Definition 1
b) From looking at the graph, you can tell that is one-to-one because it should pass both a vertical AND horizontal line test.

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Video Transcript

all right, What's the 1 to 1 function? First of all, noticed that we use the word function. And so because of that word, we know that it's something where every X value has exactly one y value. One. Why value for each X value in the domain? But what's the 1 to 1 part? Well, the opposite has to be true one X value for every Y value in the domain. So every X value has one Y value. Every y value has one X value. That's a 1 to 1 function. What does it look like? So let's have one example that's 1 to 1 and one that's not 1211 X value for every X value one y value for every X value one X value for every Y value. We know that if it's a function, it has one y value for every X value, and it passes the vertical line test. And if it has one X value for every Y value, it passes the horizontal line test as well. That would be 1 to 1, not 1 to 1. It might still be a function, so it's still passes the vertical line test. That could happen, but it doesn't pass the horizontal line test