This reviewer includes the following topics: - Other Types of Functions *Square Root Functions *Rational Functions *Logarithmic Functions *Identity Functions *Constant Functions *Absolute Value Functions - Inequalities - Permutations - Circular Permutations - Probability

1. NATIONAL ACHIEVEMENT TEST
REVIEW 2015
(MATHEMATICS)
Prepared by:
Ms. Ma. Irene G. Gonzales

2. OTHER TYPES OF FUNCTIONS
1. SQUARE ROOT FUNCTIONS
Form:
Domain:
Range: (if the form is )
(if the form is )
xxf )(
 0xx |
 0yy |
 0yy |
xxf )(
xxf )(
(Gonzales, 2015)

3. (Gonzales, 2015)

4. (Gonzales, 2015)

5. OTHER TYPES OF FUNCTIONS
2. RATIONAL FUNCTIONS
Form:
Domain: Values of x that are real except the value that
makes the denominator equal to 0.
)(
)(
)(
xD
xN
xf 
(Gonzales, 2015)

6. OTHER TYPES OF FUNCTIONS
2. RATIONAL FUNCTIONS
Form:
Range: If the highest degree of the numerator and the
denominator are equal, divide the coefficient of the
highest degree of the numerator to the coefficient of
the highest degree of the denominator.
)(
)(
)(
xD
xN
xf 
(Gonzales, 2015)

7. OTHER TYPES OF FUNCTIONS
2. RATIONAL FUNCTIONS
Form:
Range: If the highest degree of the numerator is less than
the highest degree of the denominator, then the range
is .
)(
)(
)(
xD
xN
xf 
 0yy |
(Gonzales, 2015)

8. OTHER TYPES OF FUNCTIONS
3. LOGARITHMIC FUNCTIONS
Form:
Domain:
Range:
xxf
alog)( 
 0xx |
 Ryy |
(Gonzales, 2015)

9. (Gonzales, 2015)

10. (Gonzales, 2015)

11. OTHER TYPES OF FUNCTIONS
4. IDENTITY FUNCTIONS
Form:
Domain:
Range:
xxf )(
 Rxx |
 Ryy |
(Gonzales, 2015)

12. OTHER TYPES OF FUNCTIONS
5. CONSTANT FUNCTIONS
Form: Graph: horizontal line
Domain:
Range:
cxf )(
 Rxx |
 cy 
(Gonzales, 2015)

13. (Gonzales, 2015)

14. OTHER TYPES OF FUNCTIONS
6. ABSOLUTE VALUE FUNCTIONS
Form: Graph: v - shaped
Domain:
Range:
xxf )(
 Rxx |
 0yy |
(Gonzales, 2015)

15. INEQUALITIES
INEQUALITY SYMBOLS
☺less than
☺greater than
☺not equal to
☺less than or equal to
☺greater than or equal to
(Gonzales, 2015)

16. Examples
1. In how many ways can you arrange the
letters in the word “heptagon”?
2. In how many ways can you arrange the
letters of the word “happy”?
(Gonzales, 2015)

17. Examples
3. In how many ways can a committee of
three be formed from a group of 10
members?
(Gonzales, 2015)

18. Circular Permutation
1. How many ways can you sit 5 people in
a round table with 5 seats?
(Gonzales, 2015)

19. PROBABILITY
- field of mathematics that deals with chance.
P(event) = n(Event)
n(Sample Space)
(Gonzales, 2015)

20. Example
1. A coin is tossed. Find:
a. the sample space
b. the probability of getting a head
(Gonzales, 2015)

21. Example
2. If a card is drawn from a well-shuffled
deck of 52 cards, what is the probability
that it is a king of diamonds?
(Gonzales, 2015)

22. Example
3. A box contains five red, two white, and
three green balls. If a ball is selected at
random, find the probability that it is
a. red c. not red
b. green d. black
(Gonzales, 2015)

23. Example
4. A card is selected at random from an
ordinary deck of playing cards. Find the
probability that the card is
a. a heart c. a 4 or an 8
b. is black d. a red queen
(Gonzales, 2015)

24. Example
5. A large box contains 365 tickets, one for
each day of a common year. Suppose one
ticket is selected at random.
a.) Find the probability that the selected
day is in December.
b.) Find the probability that the selected
day is your birthday.
(Gonzales, 2015)