Given the graph of F of X,
graph G of X equals F
of the quantity X minus five plus four.
When we are given G of X equals F
of the quantity X plus C plus D,
the value of C indicates a shift left or right,
the value of D indicates a shift up or down.
If C is less than zero, then we have the form X minus C
and the graph is shifted right C units.
If C is greater than zero, then we have the form X plus C
and the graph is shifted left C units.
If D is less than zero,
then the graph is shifted down D units
and when D is greater than zero,
the graph is shifted up D units.
Notice how the shift left or right is
in the opposite direction we might think.
When we have subtraction, the graph is shifted right,
when we have addition, the graph is shifted left.
So going back to our example.
Because G of X is equal
to F of the quantity X minus five plus four,
the X minus five indicates a shift right five units.
And then plus four
on the end indicates a shift up four units.
And because we have a segment,
we can simply translate both endpoints,
right five and up four, to determine the graph of G of X.
Starting with the leftmost endpoint,
that has an ordered pair negative three,
comma, negative five.
If we shift the graph right five units,
and then up four units,
this would be the new endpoint.
And now, for the second endpoint
that has the ordered pair negative one, comma, two,
again, we will shift it right five units
and up four units.
So moving right five
and up four.
We have the second new endpoint.
So the graph of G of X is this blue segment here.
Another way to determine the graph of G of X is
to perform arithmetic on the two endpoints of F of X,
starting with the endpoint negative three,
comma, negative five.
If we want to shift this point right five units,
we would add five to the X coordinate.
If we want to shift it up four units,
we would add four to the Y coordinate.
And let's go ahead and do that.
We would have negative three plus five for the X coordinate
and negative five plus four for the Y coordinate,
which gives us the ordered pair two, comma, negative one,
which, notice how it is one of the endpoints for G of X,
this point here.
Similarly, for the other endpoint of F of X,
we have negative one, comma, two.
To shift this point right five and up four,
once again, we would add five to the X coordinate
and add four to the Y coordinate.
Which gives us the ordered pair four, comma, six,
which is the other endpoint for G of X.
Let's take a look at one more example.
We're given the graph of F of X
and we're asked to graph G of X equals F
of the quantity X plus two minus three.
The X plus two indicates the graph
of G of X is shifted left two units
and the minus three
on the end indicates the graph has shifted down three units.
And again, because we have a segment,
we can simply translate the two endpoints
to find the graph of G of X.
Notice the leftmost endpoint
has the ordered pair negative two, comma, four.
The rightmost endpoint
has the ordered pair five, comma, two.
So shifting the point of negative two, comma, four
left two units and down three units.
We would have this point here
where the ordered pair is negative four, comma, one.
And if we shift five, comma, two left two and down three,
we're at this point here
where the ordered pair is three, comma, negative one.
And therefore,
G of X is the graph of this blue segment here.
I hope you found this helpful.