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Numerade Educator

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Problem 12 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) = \sqrt[3]{x} $

Answer

$\operatorname{yes}(1$ to 1$)$

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Video Transcript

we're deciding whether or not this function is 1 to 1. So to do that, let's imagine the graph. The graph of the cube root of X looks like this now to be oneto. One means for every X value. There's only one Y value, and for every y value, there's only one X value, so it must pass the vertical line test and pass the horizontal line test. So checking the vertical line test pass a vertical line through it only passes through one point, not more than one. So that's a pass. And for the horizontal line test, pass a horizontal line through it cannot pass through more than one point. That's also a pass. So, yes, this one is 1 to 1.