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Problem 11 Easy Difficulty

A function is given by a table of values, a graph, a formula, or a verbal description. Determine whether it is one-to-one.

$ g(x) = 1 - \sin x $

Answer

function is not one-to-one.

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Video Transcript

we're deciding whether or not this function is 1 to 1. And to be 1 to 1 means that every X value has only one y value. And every y value has only one X value. So one way to figure it out is to look at the graph. So imagine this graph. First of all, imagine a sign graph, Michael. Sign of X would look something like this and then imagine that you flipped it upside down and got y equals negative sine of X. So that would look something like this. And then imagine that you shifted it up one. And that's where we get G of X. So that would look something like this. Okay, well, does every x value have only one y value and every y value have only one X value? Clearly not because if we pass a horizontal line through, it passes through multiple points. That means there are multiple X values with the same y value. So this is not 1 to 1