Given g of x is equal to 8x plus 2, find g of zero,
g of negative 5, and g 2x plus 3.
So all this is, when they say g of x is equal to 8x plus 2,
this is a function definition.
They're saying you give me any x,
and you input it into my function g,
and my function g will output, will associate with that number
x, another number that happens to be 8x plus 2.
This is one way to create an association.
It's going to associate if you were to put 1 here.
If this x is 1, you're going to do 8 times 1 plus 2.
So you would associate 1 through g.
You'd associate 1 with 8 times 1 plus 2, which is 10.
So it's just another way of creating association
that you could do with sets of ordered pairs
or you could do it graphically.
But this is one of the most typical ways
you'll see a function defined.
It says, look, input an x over here
and I'm going to output 8x plus 2.
So with that out of the way, let's think
about what the g of 0 is.
g of 0 literally just means we're
inputting 0 into this function.
And this function says, whatever your inputting,
I'm going to output 8 times that plus 2.
So g of 0 is going to be-- let me write it this way
so it becomes clear what I'm doing. g of 0
is going to be 8 times is 0 plus 2.
So wherever we saw the x, we replaced it what it
with whatever we're inputting.
That is our x in this situation right over here.
And so this is equal to 8 times the 0 plus 2
is just equal to 2.
So g of 0 is equal to 2.
Let me just write that here. g of 0 is equal to 2.
Now let's try g of negative 5.
So let me write it this way.
I'll write it, g of negative 5 is equal
to-- I'll try to do the color-coding a little bit
better this time.
It's going to be equal to 8 times our x, which
in this case, is negative 5.
8 times negative 5 plus 2.
We're inputting x-- We're inputting a negative 5.
And we're going to output 8 times negative 5 plus 2.
Wherever we saw the x, we just replace it with a negative 5.
And this is just equal to 8 times
negative 5 is negative 40 plus 2 is equal to negative 38.
So I'll write this over here on the right.
We have g of negative 5 is equal to negative 38.
Now, this last one is a little bit interesting.
So we just did this one.
Now, let's do g of 2x plus 3.
So now they're not inputting a number.
They're inputting an expression.
Now, what we have to do is everywhere where we see x here,
we're going to replace it with that expression.
If I did g of a circle-- let me write this down.
If I did g of an orange circle right over here.
By this function definition, if I'm
in putting an orange circle, I should
output an orange circle 8 times the orange circle,
which doesn't make a lot of sense.
But hopefully you get the idea that whatever you're inputting,
you're just going to multiply it times 8 and add two.
So if we input 2x plus 3, we're going to output this times 8
plus 2.
Wherever we see an x, we replace it with this right over here.
So let's try that out.
So now we have g of 2x plus 3 is going to be equal to 8 times
whatever we're inputting, eight times
whatever inputting plus 2.
If this was an orange, we'd put an orange here.
If this is a negative 5, we put a negative 5 here.
If this is a 0, we put a zero here.
In this case, we're inputting 2x plus 3 into our function.
So we put 2x plus 3 where x is right over there.
So 2x plus 3.
Whatever we input, this function says multiply by 8 and add 2.
We're inputting 2x plus 3, multiply it by 8,
and then add 2.
And so this is going to be equal to-- we just distribute the 8.
And you get 16x plus 24.
And then you still have this plus 2 out over here
So this is going to be equal to 16x plus these two.
You add them up, you get 26.
So we can write over here, and I'll
do that same color so it can be consistent.
We have g of 2x plus 3 is equal to 16x plus 26.
And we're done.
I know it's going to be confusing
because you're inputting-- you're replacing
x with something that has x in it,
but you really should just view this
as if this was an orange ball or a star or even if this had
y's is it.
Wherever you see an x, you replace it
with whatever you are inputting it.
In every instance, we replace the x with 2x plus 3.