If you were to plot the points above you would see that we end up with a “V” shaped plotted line identical to the absolute value parent function above, albeit with the vertex located at (-2, 0).Graph of y = |x + 2| Notice also that you could have used any values for x, ...
mathematics is focused on the end point: the answer, the solution, the proof. We attach so much emphasis on the destination — the more efficient the better. We place such high value on the final moment of the mathematical process; this is reflected in the language we choose to define ...
To avoid all these iterations, we could find the tangent position directly, add a little margin to it, and move the entity there. But, for this tutorial, we'll just use the stupid iterative approach to keep things simple. With this method, there's no "terrain metadata" at all. We sim...
While we all know that nothing will ever be as effective as engaging in problem based math learning in a face-to-face environment, this experience is a great opportunity for us to sharpen up our tech skills and think of ways that we might use them to enhance our lessons once we’re bac...
Finally, PointBmoves along the line connecting betweenR0andR1. This point moves along the path of the animation. Source:Wikipedia If you want to have a better feel for how cubic beziers work, I recommend checking outthis desmos link. Play around with the control points and check how the ...
In many situations, it’s better to use Bernstein polynomials rather than anexplicit functionof the form y = f(x), because of the limitations offunction notation. These include the fact that a vertical line (i.e. avertical asymptote) x = c cannot be described using function notation. ...
Function transformations give us sets of mathematical operations we can perform on functions to shift or distort their graphs into other forms. The usual function transformations are translation (just moving the graph), dilation (stretches or compresses ...
I think this shows that the information contained by the Taylor series is enough to end all the way to a singularity on the real line, rather than being limited by the distance to a singularity in the complex plane. The only time this wouldn't work is if the set of points on th...
First, we need to cover a little bit of wave theory to make sure we are all on the same page. The following examples are chosen for a reason that will hopefully become clear when we get back to the XLR discussion. I will useDesmos online graphing calculatorto generate graphic examples. ...
Human airway epithelial (HAE) cellular models are widely used in applicative studies of the airway physiology and disease. In vitro expanded and differentiated primary HAE cells collected from patients seem to be an accurate model of human airway, offeri