You should know all basic trig graphs (sin, cos, tan), quadratics, cubics (relatively simple ones), x^n, logarithmic graphs (I believe only base e and 10 are listed - may want to check this), exponential graphs, piecewise functions (just a combination of the previous list) and also how the addition of the various types of graphs works (search addition of ordinates for more information).
For all these graphs you should also understand how to graph transformations of them as well.
Page 71 in the Mathematics Study Design document is where this is listed.
However, addition of ordinates is more of a luxury to learn as it's not tested much. Everything else mentioned by FelixHarvey is essential.
I must note that the graph of any exponential graph involving an exponential of any base is just a series of transformations away from the graph of y = e
x, and similarly, any log graph is also just a series of transformations away from the graph of y = log(x).
Hey, I was just wondering, what are all the types of graphs that need to be memorised for 3/4? Like being able to draw them without the use of a CAS. I’ve only completed 1/2 (hence I only know a few of the more basic ones). I was doing some 3/4 preparatory questions (simple stuff like the implied domain when looking at a function) and I realised that some of the graphs I had to plot on the CAS because I had no idea what they looked like, unlike others which I could tell in my head.
Is there a list of graphs anywhere or something?? I’d like to learn how to graph all of them over the break because I always find myself falling behind in class when my teacher introduces a new graph.
Thanks to whoever answers!!
For implied domains, you should generally be able to tell by looking at the function and asking yourself, what requirement needs to be satisfied for this thing to make sense? Let us consider a toy example.
It looks complicated. However, the trick is to note that there is a square root, and that you can't square root anything you want; the thing you're trying to square root can't be negative. Thus, you have the inequality
The issue is, you'd like to multiply top and bottom by x+1, but you don't know if it's positive or negative, so the inequality sign could flip. So, let's just assume x+1>0 and multiply. Now that it's positive, the inequality sign does not flip, and we find x >= 1. We assumed x + 1 > 0 too, so our solution is x >= 1 and x > -1, or just x >= 1.
What if x + 1 < 0? Now, the inequality sign flips, and we find x <= 1. We assumed x + 1 < 0, so x <= 1 and x < -1, which requires x < -1. So our total implied domain is
Be careful of the inequality signs; one doesn't include -1, one includes 1.
You can play a similar trick with fractions. Fractions are ok whenever the numerator is defined and the denominator is defined but nonzero. Most functions, like rational functions, tangents, logs, square roots will all have some restriction on what goes into them. You need to take those into account.