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### Course: Multivariable calculus>Unit 1

Lesson 5: Transformations

# Transformations, part 1

One fun way to think about functions is to imagine that they literally move the points from the input space over to the output space. See what this looks like with some one-dimensional examples.  Created by Grant Sanderson.

## Want to join the conversation?

• Is there a more accurate term for transformations? Doing a google search all I can find are the basic shifting, scaling, rotation, et.c?
• Multidimensional input or output. Parametric Functions is a more accurate term for transformations.
• how do you do rotations?
• Why does he say at , that you lose input information in a parametric plot?
• Because when you look at a parametric curve or a parametric surface, you are only looking at the result of the function/transformation, that is, you are looking in the output space of the function, and many different parameterizations exist for the same resulting output curve or output surface.
For example, r(t)=[t t^2] and s(t)=[3t^2 9t^4] both appear as the same parametric curve on the x-y plane even though they are different parameterizations of f(x)=x^2. The reason Grant says you "lose input information" is because you don't know anymore what the specific range of t-values were that got mapped to the parametric (curve, in this case). Especially if I didn't tell you what those two parameterizations were initially, you would have no way of knowing if you just saw the parabola or a segment of it.
• Hello Grant, is there some online tool for animating functions like in ?
• Shouldn't the second graph have some vectors in it in some way?
(1 vote)
• hi idk if you'll see this but the graph on the plane traces the tip of all the vectors of each input (vectors starting at the origin)
(1 vote)
• what are the different types of Transformations
(1 vote)
• Please, share the name of the software being used for animation. We will try to get it.
Thanks,
Kalaivanan R
(1 vote)
• at you said "that just a one-dimentional fonction ,it will have a single variable input and it will have a single variable output" ,but this is the definition of two-dim fonction?!
(1 vote)
• is there transformation for a lesser level eg : 8th grade
(1 vote)