An archive the questions from Mark's Fall 2018 Calc I Course.

What’s your favorite function?

Mark

(5 pts)

The purpose of this assignment is to provide a gentle introduction to using this system. The assignment is simple: Tell me your favorite function, in nice mathematical notation, and include a computer generated graph. For example:

My answer:

My favorite function is f(x)=e^(-x^2). I can plot its graph using Sage like so:

plot(e^(-x^2), (x,-3,3))

Comments:

My answer is the stuff between the bold My Answer and the bold Comments. You should be able to format your answer in a similar fashion. Be sure to read how to do so in the About this site category. In particular, you’d want to read:

I chose to graph this particular example with the Sage cell server because it’s pretty easy to use and has a nice, publicly available, web-based interface that I can link to. Another tool that’s even easier to use and produces awesome graphics is Desmos. There are many other graphing tools that you can use, though.

audrey

My favorite function is y=cos(x). I think I’ll graph it with Desmos:

Thomas

My favorite function is (x^2 + y^2 -1)^3 - x^2 y^3 = 0. I’m gonna use desmos to show you why
.

creamcake

My favorite function is y = cos(x^3)*8 Here’s why:

haleymlindsey

This is my favorite function, y = sin(x)^5 graphed using Desmos.

Mark

@haleymlindsey and @creamcake Those functions and graphs look awesome!! Before I give those a like, could you please hit the edit button and wrap the math input in percent symbols? That will typeset that math.

For example, if I type this:

y = sin(3x^2)

I get this: y=sin(3x^2).

But if I type in the percent symbols like so:

%y = sin(3x^2)%,

Then I get

y = sin(3x^2)

See the difference??

Lane

My favorite function is y=x⋅sin(10000x). I will use desmos to demonstrate.

aallen8

My favorite function is y=mx+b simply for its simplicity. I will use desmos to graph it:

Mark

@aallen8 That’s pretty cool! Did you use specific values for the parameters m and b?

If so, can you include that info so I can give this a like?!

DustinS

My favorite function is x=sin(3t) I will show you by using desmos.

Serb

My favorite function is sin(sinx+cosy)=cos(sin(xy)+cosx)

hgriffin

My favorite function is y=x because it is the easiest function to graph. If you do not know what the graph looks like I attached one below:

Jballard

My favorite function is sin(5x)^3 because it reminds me of Asheville: full of mountains and valleys. I’ll graph it using desmos

Mark

@Jballard That looks great! Could you hit the edit button and wrap your sin(5x)^3 in percent symbols (%) so I can give it a like?

For example, if I type x^2, I get this: x^2.
But, if I type %x^2%, then I get this: x^2.

mathisfun

My favorite function is y=-1//12. Though boring, this relies on the algebraic proof that the sum of all natural numbers is equal to -1//12, based on manipulation of Grandi’s series.

SMP

My favorite function is y=sqrt(x) Here’s it on Desmos.

Emma.W

My favorite function is -X^3 due to its simplicity.

IamGamerGod

My favorite function is y = 4sin(9x). It reminds me of using an oscilloscope.

Mark

@Emma.W That’s a pretty cool link. Can you upload the image in to this page and typeset your function? You can read how to do those things here and here.

Cottoncandy

My favorite functions are sec^-1(x) and cos^-1(x)