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Will a one-to-one function always be a decreasing or increasing function?

No, see exercises 69 and 70 .

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 1

Inverse Functions

Campbell University

Oregon State University

Baylor University

Lectures

00:53

Are one-to-one functions e…

02:18

is an exponential function…

01:12

Explain how you would dete…

02:17

Increasing Functions Is th…

01:17

If $f$ is an increasing fu…

00:35

True or false: On any inte…

01:14

Determine whether the func…

00:25

00:34

What does it mean if a fun…

So they want us to determine if a function is 1 to 1 implies that will always be increasing or decreasing. Um, and we can actually come up with a couple examples of where, like, this just doesn't hold, uh, so I'll just go ahead and create one, but you can pretty much use many others. So the first one to mean that you can kind of do is notice that I'll just have something here where it's, like, decreasing until it hits this point and so notice how this is always decreasing here. But then, from zero from this point onward, it will be increasing until we hit here. And then over here, it'll just start decreasing. So you can see how over here, this is decreasing here is increasing. And then here it's decreasing. But this is 1 to 1. So the answer for this is No. This will not always be the case, and you can probably come up with some other examples as well. But this is just kind of the first one. I kind of just like Drew out there. Or maybe I should say is 1 to 1, but not always increasing slash decreasing. So that would be our answer

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