Generating inputs and outputs of a function

So we're asked to pick any three pairs of corresponding input and output values of the following function and fill the table accordingly, and if necessary, round our answers to the nearest 0.1.

Our function is defined as: if I input a t, what I'm going to output f of t is going to be negative 2 times my input negative 2 times t plus 3.

So we can just pick three arbitrary t's, input them into our function, and see what the function spits out. Well, we could go picking some really easy t's to compute.

So, for example, if t is equal to zero, then f of t, we could do this in our head, but it would be negative two times zero plus three. Well, negative 2 times 0 is just going to be 0 plus 3 is just going to be 3.

If t is 1, well then f of t is going to be negative 2 times 1. I'll write it in parentheses plus 3. Well, negative 2 times 1 is negative 2 plus 3 is 1. So this is 1.

And just for kicks, we could even put a negative 1 here. Once again, I could have put in crazier numbers; I could have put in 2.30789, but that would just be more computation. Might as well pick some easy numbers. We're just trying to get a feel for this function: depending on what I input, what do I output? And I'm allowed to pick my inputs.

So if it's negative 1, it's going to be negative 2, so t is now negative 1 plus 3. So negative 2 times negative 1 is positive 2 plus 3 is 5. It's going to be positive 5.

Let's do a few more of these. So it says choose any three points on the following graph of y is equal to g of x and fill the table, so each column represents a point. If necessary, round your answer to the nearest 0.5.

So once again we could see well there's a bunch of interesting points here. If x is equal to 0, what is g of x? This is y is equal to g of x. We see g of x is equal to negative one. Actually, let me make this a little bit smaller so that we can see it all on one screen.

So there we go. Now we should be able to see it a little bit easier. So, if x is zero, and once again I'm just picking 0 because it's easy to see that when x is 0, y is equal to negative 1 and y is equal to g of x. So g of 0 is negative 1. See that right from the graph?

Let's see some other points. So we have this point right over here. When x is negative 1, y, which is equal to g of x is equal to 2. The point (1, 2) is on this line: when x is 1, y is 2, and y is equal to g of x, so g of 1 is 2.

All right, let's pick another one here. Let's see: when x is 1, y is negative 4. When x is, sorry, this was negative 1 right over here. When x is negative 1, y is equal to 2, and when x is positive 1, y would be equal to negative 4.

And actually, let me, these are the exact same numbers that I used last time for the inputs. Let's just see that you don't have to, you know, I could use these numbers, but I could pick different numbers.

I could say, let's see, this number, this point over here is interesting because it looks like both the x and y coordinates are integers. So if x is negative 3, y is 8. So, if x is negative 3, y is 8.

So once again, you should try to pick some values where you can clearly see what the corresponding x and y coordinates are of that line. But any of those would be valid pairs for a given input. What's g of x going to actually be?