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# In mathematics, a horizontal function is a function whose graph is a horizontal line. Such functions are important in the study of differential equations, because any horizontal function is the zero solution of a homogeneous linear differential equation.

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tens of trigonometry functions. And the first transformation we're going to talk about is the horizontal shift Basically meaning from our parent function graph. Is it going to shift to the left or is it going to shift to the right and you can tell this based on our functions? And so what you're looking for is you're looking at the function and you're looking in this parentheses where angle is either being is subtracted by h H is that horizontal shift and what you're wanting to look for if you want to look for the actual number H don't worry about the minus, son. Look at just H. If h is greater than zero, meaning is positive. You're going to shift to the right. If H is less than zero, you're gonna shift to the left. So, for example, if I have, if I have a cosign graph here similar to this one right here and my H was positive, But whatever degrees, I could shift it to the right each point, which means my new graph would look something similar. Shoot this one. So this is what we mean about horizontal shift. So we're going to draw on original one and then we're gonna graph over that. If you're doing this on paper, I do strongly recommend using different colors because it'll kind of help you see your new graph. So let's look at this one. Why equals co sign? I'm sorry, This is actually supposed to be signed, not co sign off the angle minus 60. And I've already drawn the graph out. Here's a son. This is just the parent function off all we're going to Dio. So what we're gonna do is we want to go ahead and look at our H and in this case are h is 60. And since 60 is greater than zero, like we said, if it's greater than zero, we're going to shift it to the right and we're going to shift it 60 degrees to the right. So this means that where I have the 90 we'll shift 60 degrees to the right. So let's start where x zero, and basically just to kind of let you know, it's every other markets 90. And then this mark is to 70. So we're gonna be kind of in between places. I'm gonna do this a different color. So for the first one. Let's do from zero. So we need about 60. So it's gonna be approximately right here, so we'll move everything about that many times. That much over each little hash mark is about 45 degrees. So just to kind of get a concept of where we need to move it, so this will kind of be where this needs to go. So then I'll kind of show you the horizontal shift, and I kind of did go ahead and add another point just to kind of show the entire thing. This is what a horizontal shift. It shifted about 60 degrees to the right. Now, sometimes you have radiance, so that would affect how you label it. But if you're not sure, you don't feel comfortable. Radiance. I do recommend changing your radiance two degrees and graphing it that way because you can also graph it from there Liberty University

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##### Top Algebra 2 Educators ##### Lily A.

Johns Hopkins University ##### Alisa L.

University of Texas at Austin

AH
##### Ahyeon H.

University of California, Berkeley ##### Boris M.

University of North Carolina at Chapel Hill