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Graph Vertical Transformations

In mathematics, a transformation is a rule, operation, or a process that maps elements of one set (the domain) to another set (the range). For example, a linear transformation is a rule that takes a vector in a space and transforms it to another vector also in that space. A vertical transformation is a transformation in which the output is a scalar multiple of the input.

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trigonometry graphs and we're gonna look at vertical shifts. Now, here, we're gonna look at a couple different things. With this, we're gonna add one more element to our functions. And this time we're gonna add this, adding the K R K is going to determine our direction of going up or down. But K also tells us a midline and a midline is gonna basically is kind of thinking about drawing a new um X axis is kind of the best way I can describe it. It's not your X axis, but it's kind of drawing that new line to represent it on this vertical shift. Mhm and basically very similar to the horizontal. If you're K is greater than zero, you're gonna shift up. K is less, you're going to shift down, and it's gonna be all based on this midline, which is your K. So let's look at this one. Where have why? Why sign minus one now for this one, R K is gonna be negative one, which means we're gonna have a midline of negative one. So our X axis, of course, is obviously where x zero. So I'm gonna go ahead and draw a midline. We're at negative one. And this is a son. So I'm gonna go ahead and draw the sign graph out. This is what the sign graph looks like. And then if I go back animal kind of retouch this mid. Alright, so there's my midline. So basically, what I'm gonna do is I'm going to shift everything one down one basically where everything if it crosses the X axis, is now gonna be on the midline. So we do this color right here, so I'm gonna shift everything down those and so everything else will come down one as well. So now my new graph is going to be right here, So there's my vertical transformation.

Liberty University
Algebra 2

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Top Algebra 2 Educators
Alisa L.

University of Texas at Austin

Boris M.

University of North Carolina at Chapel Hill

Monique R.

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Heather Z.

Oregon State University

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