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# In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x). A function whose domain is a subset of the real numbers is called a "real-valued function". A function from a set X to a set Y is a subset of the Cartesian product X × Y that preserves the ordering, that is, if "x" is in "f" then so is "y" for any "y" in Y. Such a function is called "continuous" if the preimage of every neighborhood of a point "x" in X is a neighborhood of "f"("x") in Y. A function from the real numbers to the real numbers is called a "continuous function". However, most commonly encountered functions in calculus are "discontinuous", which means that they are defined only on a subset of the real numbers.

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Arco 2nd, 2nd and co tangent functions. Now the first thing to remember about the co second the second and the Tennco tangent functions is they are all reciprocal. For example, remember that sign is our Why over our whereas co second is the reciprocal, it's the are over the why the second the cosign is X over our and second is our over X and co tangent tangent, remember is why over X and co tangent is X over. Why? So they're all reciprocal and we're gonna use that in our graph and basically, how we're going to start. This is we're going to kind of start these little use shapes, and the first thing we're gonna do is we want to start off graphing these first. So like, here's a co second while I've got graft A sign graph. Here's the sign You wanna have that son graph draw just like for the second, we wanna have a co sign graph draw and then for co tangent, we wanna have a tangent graph draw. So it's really critical to go ahead and draw those. So when first thing we wanna do is we wanna place are asking heights where the sun crosses the center. Basically meaning on those, um, where it crosses that center line are basically where it crosses that X intercept. So on draw these dotted lines at these points. So for our coastline, we're gonna make thes use, and they're either gonna be upward or downward. They're gonna kind of look like parabolas, and they're gonna be going towards these dotted lines. So basically, for Kasab is gonna look like this right here. And even if the graph kept going, we would continue adding the Jews for a second. We're gonna kind of do the same thing for a second where we have those X intercepts, we're gonna draw these dotted lines and then we're gonna draw our use. And these years we're gonna be at these maximum and minimums. And so there's a second. So both of those show the reciprocal of our Coty, and it's basically it's showing where is going in the opposite directions from those points of those maximums and minimums Now, co change, it's gonna be a little bit different. We've already got these dotted lines, so we're gonna kind of basically draw them kind of going in the opposite direction. So, for example, for our first one, we would draw it going downward from here. Our lines would go in the opposite direction, and we would even have Are you here? But it would kind of just not be seen. So all of these showed the co tangent, which is like I said, It's basically the reciprocal, so it's gonna be going in the opposite direction with thes use. Liberty University

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##### Top Algebra 2 Educators ##### Alisa L.

University of Texas at Austin ##### Martha R.

Michigan State University  ##### Heather Z.

Oregon State University