Big Ideas Math [IM1]: 3.3 - Function Notation (Lecture & Problem Set)

Publicado el: 09 septiembre 2024
en el canal de: Mr. Robinson's Virtual Math Classroom

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Function notation, y = f(x), may appear scary to begin with, but I promise you that it isn't once you grasped what it is. Function notation is NOT going away in future math classes, and up through calculus you will absolutely use it consistently. I suppose it's best that you learn it now. ;)

f(x) is just pronounced as "f of x," which is a way of saying that "y is a function of x." We can use any other letters we'd like as well, such as g(x), h(x), r(x), t(x)... etc. You'll see the problem set use plenty of examples with different appearances of inputs and outputs.

What we do with it is straightforward: we substitute a number for our input, and generate an output. So an equation that says y = 2x - 7 could also be written as f(x) = 2x - 7, and when they ask for f(-3), they're just asking the question: "What is y when x = -3?" That's it and that's all, nothing more! When you get f(-3) = -13, that means there is a point on your graph that is (-3,-13). Using that same example though, if they asked to find x when f(x) = 11, you'd have to substitute 11 for f(x) so the equation says 11 = 2x - 7 (in which case, x = 9).

We'll also be dealing with function notation in situations that do not contain an equation itself, but rather just the concept of inputs, outputs, and making sense of the notation. Maybe C(h) could represent the cost of producing d amounts of headphones, so if you look at C(100) - C(30), you're looking at the cost difference of producing 100 vs. 30 headphones. Little things like that!

I want to warn that I accidentally copy down #17 incorrectly (I fix it while doing #18), and that on #30 I told myself that 130 + 60 = 190 and 160 + 60 = 190... I figure it out a minute later and fix it. This was a long day of recording. :p

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PDF DOWNLOADS

Textbook (3.3): https://smallpdf.com/file#s=d9c7a3af-...
Graph paper (scaled): https://docdro.id/flV4fYe

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TIMESTAMPS (separated by section)

(0:00:00) Introduction
(0:01:05) Lecture overview
(0:14:03) Problem #1-2
(0:15:27) Problem #3-10
(0:23:44) Problem #11-12
(0:30:27) Problem #13-18
(0:36:25) Problem #19-20
(0:37:41) Problem #21-22
(0:41:12) Problem #23-28
(0:48:06) Problem #27-28
(0:53:29) Problem #29-30
(1:00:30) Problem #31
(1:02:56) Problem #32
(1:04:47) Problem #33
(1:07:50) Problem #34
(1:13:37) Problem #35
(1:14:68) Problem #36

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