Rapunzel is a princess locked in a tower by her evil stepmother. She dreams of seeing the floating lanterns that appear every year. Her stepmother agrees to let her go if she solves math equations on the tower wall. Rapunzel finds a magical book that teaches her about functions and how to add them. She uses this knowledge to correctly solve the equations and gains her freedom from the tower.

2. Once upon a time, in a far away land,
there lived a very beautiful princess
named Rapunzel. Her life is different
from other’s lives because she doesn’t
have her freedom. She was locked up by
her evil stepmother in a tower.

4. “How I wish I could come
nearer to see those flying
lanterns and could fly one”

5. My dear
Rapunzel, I’m
home!

6. Mother, can I leave the tower
to see the floating lights from
the outside world?

8. Mother
p-l-e-a-s-e!

9. I will allow you if and
only if you’ll be able to answer
the mathematical equations
written on the wall above the
tower.

10. But how can I
answer those
equations mother?
Find the magical
book my dear, that
will help you a lot to
answer the
equations.

11. But how can I find the
magical book on these
huge number of books?

12. Whoah! At last, I
found you!

13. What is FUNCTION?
A function is
like a machine that
has an input and an
output.
It is written as
f(x) where the value
of x is just a place
holder. For example,
f(x)=2x2 –x then the
value of x is 2
so we should
substitute all x with
2; f(2)= 2(2) 2-2=6 ,
we can therefore
conclude that f(x)
is equal to y.

14. That’s just an
introduction.
Let’s now
move on to
the next page,
the “SUM OF
THE
FUNCTION”
If given two
functions namely f(x) and
h(x) respectively, then
operation for these two
function can be expressed
as:
(f+h)x= f(x) + h(x)
For example; if
f(x)= 3x2-2x+5
g(x)= 3x2-8x-9
h(x)= 4x2-6

15. Find (f+h)x ;
(f+h)x= f(x) + h(x)
=(3x2-2x+5) + (4x2-6)
ADD SIMILAR
TERMS
(f+h)x=7x2-2x-1
Try to solve
(f+g)x= f(x) + g(x)
Using the same
value given earlier.
Checking:
(3x2 -2x+5) +
(3x2 -8x-9)
(f+g)x =6x2 -10x-4

16. Let the battle begin. . . . .

17. Add the following functions :
•f(x)= 2x+3 ; g(x)= 3x-1
•f(x)= x+2 ; g(x)= 2x2
•f(x)= x2-1 ; g(x)= x+1

18. As what the
magical book
says I should just
add similar terms
to answer them.
Let’s try it first!

19. •(f+g)x= f(x) + g(x)
=(2x+3) + (3x-1)
= 5x2+2
=x3
•(f+g)x = f(x) + g(x)
=(x+2) + (2x2)
=2x3+2
•(f+g)x= f(x) + g(x)
=(x2-1) + (x+1)

20. Rapunzel dear,
yoohoo, I’m home.
Did you finish
answering he
equations written
on the wall?

21. Yes mother, my
solution is
written on the
paper beside the
mirror.

22. •(f+g)x= f(x) + g(x)
=(2x+3) + (3x-1)
= 5x2+2 CORRECT
CORRECT
CORRECT
•(f+g)x = f(x) + g(x)
=(x+2) + (2x2)
=2x3+2
•(f+g)x= f(x) + g(x)
=(x2-1) + (x+1)
=x3

23. How did you
answer it
correctly my
dear?
I learned it from the magical
book mother. So does that
mean I can already leave the
tower and watch the flying
lights?

24. The evil Mother Gothel turned into ash and
Rapunzel got her freedom.
Ugh. NO WAY! This
is not happening! I
won’t allow it.

25. I’m
freeeee!
Weeeee!
!!

26. THE END

27. Hope you’ve learned a lot.
Micro-lesson about “Sum of Functions”
Project in Math IV
Submitted by:
Ma. Ysabel M. Francisco
Lovejoy Lugtu
Jessa May Recote
IV-Diamond
Submitted to:
Mr. Eric De Guzman