Question

I would like to know how to work functions.

Answer 1

[1] First, we need to review how to work with function notation. When we write f(3) = -4, for example, what we mean is that when x = 3, y = -4. If we ask for the value f(6) = ? what would we get? Well, that means when x = 6, y = ? and looking at the table, we see that y = 5. So, f(6) = 5.

[2] Now, the question is a little tricky, they say, "Alright, Smarty, how do you like this?" and give us y = f(1/5 * x). Uh.... 

Well, it's not too hard. But we need to be tricky. Let's start with an easy one. When x = 0, then f(1/5*0) = f(0), but we know that f(0) = 3 since we can look that up on the old table. So, we can add this row to our new table:
x = 0     y = 3

[3] Cool, let's try another... um... say x = 1. When x =1, then f(1/5*1) = f(1/5). Oh no... but I can't look that up on the old table! There isn't an row that has x = 1/5.

But, don't panic! Let's see. I do know that when x = 3, y = -4. But, how can I use that?

Aha! Let's pick x = 15. Now watch this closely. Then, f(1/5*15) = f(3), and we know that f(3) = -4 from the old table! Yesss! We've got another new row:

x = 15     y = -4

[4] By repeating this process for the rest of the rows, we can get as many new rows as we want. Let's try to use the old fact that x = -1, and y = -2. Since I have the new function f(1/5*x), I need to pick a new x so that I get a -1 somehow. I'll pick x = -5. Then, f(1/5*-5) = f(-1). And I know that f(-1) = -2 from the old table. So my new row is:
x = -5   y = -2

See if you can get the rest! Good luck! : )