- [Voiceover] 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 answer to the nearest 0.1,
and our function is defined as if I input a t,
what I'm going output f of t is going to be
negative two times my input,
negative two times t plus three,
and so we can just pick three arbitrary t's
and input them into our function
and see what the function spits out.
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 two times zero is just going to be zero,
plus three is just going to be three.
If t is one, well then f of t is going to be
negative two times one, I'll write it in parentheses,
plus three.
Negative two times one is negative two
plus three is one.
This is one.
And just for kicks, we could even put in negative one.
Once again, I could 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 one, it's going to be
negative two, so t is now negative one, plus three.
So negative two times negative one is
positive two plus three is five.
So it's gonna be positive five.
Let's do a few more of these.
So this 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,
there's a bunch of interesting points here.
If x is equal to zero, what is g of x?
This is y is equal to g of x and 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, so now we should be
able to see it a little bit easier.
So if x is zero, and once again,
I'm just picking zero because it's easy to see
that when x is zero, y is equal to negative one.
And y is equal to g of x,
so g of zero is negative one.
See that right from the graph.
Let's see, some other points.
So we have this point right over here.
When x is negative one, y, which is equal to g of x,
is equal to two, the point one comma two is on this line.
When x is one, y is two, and y is equal to g of x.
So g of one is two.
All right, let's pick another one here.
Let's see, when x is one, y is negative four.
When x is, sorry, this was negative one over here.
When x is negative one, y is equal to two,
and when x is positive one, y would be equal
to negative four, and actually, let me,
these are the exact same numbers that I used last time
for the inputs.
Let's just see that 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 three, y is eight.
So if x is negative three,
y is eight.
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?