a-function-is-given-by-a-table-of-values-a-graph-a-formula-or-a-verbal-description-determine-whet-19

Question

A function is given by a table of values, a graph, a formula, or a verbal description. Determine whether it is one-to-one.

$f(x)=x^{2}-2 x$

Amrita Bhasin · Accepted Answer

this question asked whether this given equation X squared minus two exes. One too one. We&#x27;re gonna use the horizontal line test for this. I&#x27;ve graphed this and now I&#x27;m drawing a horse. Old gentle line. As you can see, it touches the graft twice. There, for the answer is no. It is not 1 to 1.

Heather Zimmers · Answer

we&#x27;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. Why value and every y value has only one X value. So we can visualize this one, since we know is just a graph of the line with the Y intercept of negative three and a slope of two. So it looks roughly like this. So for every y value to have only one X value, it must pass the horizontal line test. If you pass a horizontal line through, it will go through no more than one point. So that&#x27;s a pass. And for every X value to have Onley one y value, it must pass the vertical line test pass a vertical line through and it only goes through one point, not more than one. And that&#x27;s a pass. So, yes, this one is 1 to 1

Heather Zimmers · Answer

we&#x27;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. And there are different ways we can look into this. We could graph it or we might be able to find some new miracle examples. So let&#x27;s try some numbers here. Let&#x27;s find f of one that would be one to the fourth power minus 16 and that would be negative 15. Now let&#x27;s find f of negative one. That would be negative. One to the fourth power minus 16. That&#x27;s also negative. 15. So look, here&#x27;s an example where we have multiple X values with the same why value? So this is not 1 to 1.

Heather Zimmers · Answer

we&#x27;re deciding whether or not this function is 1 to 1. So to do that, let&#x27;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&#x27;s only one Y value, and for every y value, there&#x27;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&#x27;s a pass. And for the horizontal line test, pass a horizontal line through it cannot pass through more than one point. That&#x27;s also a pass. So, yes, this one is 1 to 1.

Carlos Pinilla · Answer

So you&#x27;re asking you, uh, these functions Functions is want one, 12121 So but what one means either there is no Carney. There is no two points eggs worm next to so is because the two points on it&#x27;s one is different. Look, so so Well, this is, uh this is Sam buries Jerry. So no two different points get sent to the same us. It is a common situation with these. Thanks, Mom. 62 on the clubs for the same. So here your domain on your inch. Here they have the same. You should little mean I&#x27;m gruff, shall we? You know, so two different boys get mom to the same onto So this is injected until me is that, uh, it hits every point in the domain until, by definition, is gonna be on the bridge, So want the one is jerky anointed. So one. Let&#x27;s go. You want to know why? And so well, these function there&#x27;s something these farm. So you have Ah, I understand. Uh, I&#x27;m a line that is low. My three. This is their function. We&#x27;re these, uh, this conventional means that buses, they or something leftist. So if you draw any line. We only eat cigarette once. But all these functions said this fighter property. I&#x27;m also you got that you&#x27;re going to see it goes well, you can solve these equations. Why? Because then minus the X, it&#x27;s uniquely so so then over that I&#x27;m seeing because only one solution. So this function, ese indeed, wantto so? Because so, the answer is it&#x27;s 1 to 1, yes.

Amy Jiang · Answer

Okay, so in a list actors equation here is this a, um the equation of a line that is we have wise. You go to Amec&#x27;s Let&#x27;s be so we have a wire, just have to attend on a slope in the of negative three. So since we have a line, we know that this function is 1 to 1. It is off of X is a line.

Problem

A function is given by a table of values, a graph…

Problem 9 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.

$f(x)=x^{2}-2 x$

Answer

no

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James Stewart

Biocalculus Calculus for the Life Sciences

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Functions on the Real Line - Overview

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Biocalculus Calculus for the Life Sciences