X AND Y INTERCEPT

1. BENJIE S. MANGGOB
D E M O N S T R AT O R
M A R A Y A G N A T I O N A L H I G H S C H O O L

2. PRELIMINARIES

3. LOOKING BACK…
Seek and You
Shall Find

4. f(x) =
𝒙−𝟐
𝒙+𝟐
LOOKING BACK…
Given:
What is the domain?
What is the range?

5. f(x) =
𝒙−𝟐
𝒙+𝟐
LET’S LOOK BACK & PREPARE…
Given:
x -2 -1 0 1 2
f(x)
Complete the table:
undefined -3 -1 -1/3 0

6. PLOT THE FOLLOWING:
x -2 -1 0 1 2
f(x) (undefined) -3 -1 -1/3 0
(-1,-3)
(0,-1)
(1,-1/3)
(2,0)
x-axis
y-axis

7. TAKE A LOOK:
x -2 -1 0 1 2
f(x) (undefined) -3 -1 -1/3 0
(-1,-3)
(0,-1)
(1,-1/3)
(2,0)
x-axis
y-axis

8. WHAT TO EXPECT…
4. show appreciation of the lesson by actively
participating in the discussion
1. recall rational functions, domain and range of
a function
2. describe the words intercepts, zeroes and
asymptotes of rational functions
3. solve the x-intercept, y-intercept, horizontal
asymptotes and vertical asymptote of
rational functions in the discussion

9. X- AND Y -INTERCEPTS,
ZERO/ ES,
HORIZONTAL AND
VERTICAL
ASYMPTOTES
OF
RATIONAL FUNCTIONS

10. TAKE A CLOSER
LOOK…
x -2 -1 0 1 2
f(x) (undefined) -3 -1 -1/3 0
(-1,-3)
(0,-1)
(1,-1/3)
(2,0)
x-axis
y-axis

11. Y-INTERCEPT
STEPS:
1. Simplify the rational function.
2. Let x = 0, then solve for the value of f(x).

12. f(x) =
𝒙−𝟐
𝒙+𝟐
Given:
for the y-intercept: x = 0
f(0)=
𝟎−𝟐
𝟎+𝟐
= -1,
therefore (0,-1) is the y-intercept

13. X-INTERCEPT/S OR ZERO/ES OF THE
FUNCTION
STEPS:
1. Simplify the function.
2. Let f(x) or y = 0, then solve for the value of f(x) or y.

14. f(x) =
𝒙−𝟐
𝒙+𝟐
Given:
for the x-intercept or zero of the function: f(x)=0
𝒙−𝟐
𝒙+𝟐
= 0
x-2 = 0 ; x = 2,
therefore (2, 0) is the x-intercept or the zero of the
rational function

15. VERTICAL ASYMPTOTE
STEPS:
1. Simplify the rational function.
2. Find the values of x by
equating the denominator to 0.

16. f(x) =
𝒙−𝟐
𝒙+𝟐
Given:
Vertical asymptote:
1. Simplify.
2. Equate denominator to and solve for x:
x + 2 = 0 ; x = - 2

17. HORIZONTAL ASYMPTOTE
STEPS:
1. Simplify the rational function.
2. Let n be the degree of the numerator and m be the
degree of the denominator.
b. If n<m, the horizontal asymptote is y = 0, where
a is the leading coefficient of the numerator and
b is the leading coefficient of the denominator.
c. If n>m, there is NO horizontal asymptote.
a. If n = m, the horizontal asymptote is y = a/b.

18. f(x) =
𝒙−𝟐
𝒙+𝟐
Given:
Horizontal Asymptote:
1. Simplify the function.
2. n=1 and m=1, since n=m,
therefore, the horizontal asymptote is
y = 1/1 or y = 1

19. GROUP ACTIVITY
• Directions: As a group, answer this on a bond paper. After answering,
take a photo of your output to be projected on screen. One of each
group will be picked randomly to discuss your answer in front.
1. f(x) =
𝒙+𝟏
𝒙−𝟑
; solve for the y-intercept/s and zero/es or
x-intercept
2. f(x) =
𝟒𝒙𝟑 −𝟏
𝟑𝒙𝟐+𝟐𝒙−𝟓
; solve for the vertical asymptote
3. f(x) =
𝟑𝐱+𝟒
𝟐𝐱𝟐+𝟑𝐱+𝟏
; solve for the horizontal asymptote

20. Groups 1, 3 & 5 will answer item
number 1.
Groups 2, 4 & 6 will answer item
number 2.
Groups 7, 8, 9 & 10 will answer item
number 3.

22. OUTPUTS

23. GROUP 1 - INFINITY

24. GROUP 2- TM-SQUARED

25. GROUP 3- MATH GANERN

26. LET’S ENHANCE!

27. SO, THEREFORE…
How do you solve for the
intercepts and asymptotes of
a rational function?

28. WRAPPING UP…
Complete the sentence.
Today I have learned about…

29. WRAPPING UP…
Complete the sentence.
Today I have realized that…

30. POINT OF CLARIFICATION

31. ASSIGNMENT
A.Solve the following on the assignment notebook: Show your
complete solutions.
1.f(x)=
3𝑥
𝑥+2
2.f(x)=
𝑥2 −𝑥 + 6
𝑥2−6𝑥 + 8
B. On your journal notebook, write the steps in solving y-intercepts,
x-intercepts or zeros, vertical and horizontal asymptotes of a rational
function.
C. Bring graphing paper.