The unit Transformations and Functions turned out to be one of the toughest units I’ve worked through in the 32 past weeks. It took me the entire week to finish so I unfortunately didn’t start a second unit. Each section of the unit was fairly difficult, however there was one section in particular that I just couldn’t seem wrap my head around and still don’t completely understand. After spending close to 15 hours working through the unit, I finally started to get the hang of it all but, even still, I was fairly frustrated by the end the time I finished the unit test.

As a quick side note, there hasn’t been any unexpected news worth mentioning regarding the coronavirus pandemic. As I write this on Sunday, April 12^th, there are currently 1.8 million total cases worldwide. There is a substantial gap between the USA, which is sitting at 535K total cases, and the country with the second highest total cases which is Spain at 166k (Italy has the third highest at 152K). Canada right now is close to 28k total cases. Being that Canada’s population is 37.6 million, this means that 0.074% of Canadians are effected by the virus. Of course, because there hasn’t been nearly enough testing for that number to be accurate (or even close) that percentage is way off but, regardless, it’s still comforts me to see such a low percentage. Even still, I’m still fairly stressed about this entire situation.

When the week began, I was happy to finally learn the terms used to describe numbers that are written above and below and to the right of other numbers (such as in the case of exponents and logarithms respectively). ‘Superscript’ is the word used to describe a number written above and to the right while ‘Subscript’ is the word used to describe a number below and to the right. I’ve been trying to figure this out for many weeks now so I was very happy to finally have learned it.

The first section of the unit dealt with shifting functions. An example of this would be taking the function f(x) = x^2 and shifting it 2 units to the left and 3 units up. To do so, you’d rewrite the function as f(x) = (x + 2)^2 + 3. The main part of this that is tricky to understand is that, in order to move the function to the left along the X-axis (i.e. in the negative direction), you write it as (x + 2). What’s made this easier for me to understand is thinking that x must be equal to -2 in order to keep the term equal to 0 and therefore you move the function 2 units to the left. Moving the function up or down is much more intuitive and is done so by adding a positive or negative number to the end of the function.

The next section of the unit dealt with reflecting functions and function symmetry. The key things I learned in this part of the unit was that in order to flip a function across the Y-axis you change the sign from positive/negative directly in front of the x variable (ex. f(x) = (x + 2)^3 would change to g(x) = (-x + 2)^3) , and to flip a function across the X-axis you change the sign in front of the entire function (ex. f(x) = (x + 2)^3 would change to g(x) = -(x + 2)^3).

The unit then explained what are considered even and odd functions and functions that are considered neither even nor odd.

• Even
  • Typically a polynomial where each term is raised to an even degree.
    • Ex. f(x) = 2x^4 – 3x^2 – 5
• Odd
  • Typically a polynomial where each term is raised to an odd degree.
    • Ex. g(x) = 4x^5 – 8x^3 + x
• Neither
  • A polynomial that is made up of both even and odd terms.
    • Ex. h(x) = 2x^4 -7x^3

I used the word “typically” above because apparently this rule does not always work however it wasn’t explained to me in what circumstances the even/odd rule wouldn’t apply.

The hardest part of the unit for me to get through (which I still struggle to understand) came when I worked on scaling functions. I’ve scaled shapes before in geometry units and this was similar but I found it to be much more confusing. Scaling a function vertically either up or down on Y-axis wasn’t difficult to figure out but scaling the function to the left or right on the X-axis was very confusing. The questions that didn’t make sense to me asked me to, “rewrite function g(x) in terms of function f(x)”. For example, I’d be told that a function g(x) is a scaled version of f(x) and g(x) goes through the point (4, 1) while f(x) goes through the point (1, 1). In my mind, g(x) in terms of f(x) should written as g(x) = f(4x) since g(4) = f(4 * 1). This is wrong, however, and you’re supposed to think of it as g(4) = f(1/4 * 4). It’s tough to explain but suffice it to say I kept getting it backwards in my head and still struggle to think through it properly.

The unit finished off by working through questions involving scaling and reflecting functions which contained root terms, exponential terms (i.e. 2^x) and logarithmic terms. These questions were fairly difficult simply because I still don’t have an intuitive understanding of how any of those three types of terms work. I was able to slowly grind my way through each sections exercise without too much difficulty, although I had to double check my work on nearly every question. It took me two attempts to finish the unit test but, relative to the entire unit, it wan’t too tough.

This week I saw a video clip of Jordan Peterson (a psychologist who posts videos on YouTube) where he said something along the lines of, when learning a new skill/discipline, it takes years of being a “fool” at it (i.e. slowly stumbling through the basics) before you can become a master at it. He said you have to painstakingly make mistake after mistake in order to fully round out your knowledge of the skill/discipline/subject. I was very frustrated this week with how slowly I was getting through the material but thought about what Peterson said. I had to remind myself that, though at times it feels like my progress is going incredibly slowly, I’m absolutely getting a strong understanding of the basic mathematical concepts which I’ll need if I ever want to become a master in this subject. I realized that, to get to where I want to go, the truth is it couldn’t be any other way.

I have 4 units to get through to finish off this course and am still aiming to finish the course by the end of the month. It’s currently April, 13^th which gives me 18 days to get through it. This means I essentially have to get through 2 units each week to get it done. Normally I take a bit of time to think of some semi-interesting way to end these posts but, considering how little time I have to do this, I can’t be bothered. Hopefully by not having a good ending here I’ll have good news about my progress next week!