This document discusses rational functions and how to sketch their graphs using intercepts and asymptotes. It provides examples of finding the domain, intercepts, and asymptotes of various rational functions. It explains that the vertical asymptote can be found by determining where the denominator is equal to 0. The horizontal asymptote depends on the degrees of the numerator and denominator. Examples are given of finding horizontal and vertical asymptotes and sketching the graphs of rational functions.

1. THE GRAPH OF RATIONAL
FUNCTION
Using intercepts and asymptotes
JECEL C. GINGA
Frances National High School

2. 1. the set of all
values that the
variable x can take.
D I ONMA

3. 2. the set of
all values
that f(x) will
take.
N A R G E

4. 3. It is the
function
value when y
= 0
PETXNCRETI
X - INTERCEPT

5. 4. It is the
function
value when
x = 0
Y - INTERCEPT

6. TRUE/FALSE
5. f(x) = x + 3
x - 3
has a DOMAIN of
{x ∈ Ɍ⎮x ≠ 3}

7. TRUE/FALSE
6. The x-intercept
of y = 2x + 5 is 5
x - 1 2

8. TRUE/FALSE
7. The y-intercept
of y = 2x + 5 is - 5
x - 1

9. Ooops! Let’s find more
friends. Count one to four
so we can make four
groups

10. Consider f(x) = x + 3
x - 3
(a) find its domain, (b)
intercepts , (c) sketch its graph
with the given table of values
x 0 1 2 3 4 5 6
y

11. Consider f(x) = x + 3
x - 3DOMAIN:
x - 3 = 0
x = 3
{x ∈ Ɍ⎮x ≠ 3}

12. y-intercept:
y = 0 + 3
0 - 3
= 3
-3
= - 1
x-intercept:
0 = x + 3
x - 3
x + 3 = 0
x = -3

13. x 0 1 2 3 4 5 6
y -1 -2 -5 - 7 4 3

14. ASYMPTOTE a straight line
approached by a curve as a
variable in the equation for the
curve approaches infinity.
It is classified to vertical and
horizontal asymptote

15. Vertical Asymptote
Vertical asymptote can be
found by determining the
value of a where the
denominator of the function
is equal to zero, that is x = a
x + 1 = 0
x = - 1

16. Horizontal Asymptote
Let n = (degree of numerator)
m = (degree of denominator)
◦If n < m, the graph has a
horizontal asymptote at y = 0
y = 0
x
= 0

17. Horizontal Asymptote
Let n = (degree of numerator)
m = (degree of denominator)
◦If n = m, divide the leading
coefficients of the numerator
and denominator.
y = x
x
= 1

18. Horizontal Asymptote
Let n = (degree of numerator)
m = (degree of denominator)
◦If n > m, no horizontal
asymptote, but a slant
asymptote instead.
no horizontal
asymptote

19. A. x = 0
B. x = 3/2
C. x = 5/2
D. x = -5
Find the vertical asymptote of:

20. A. y = 0
B. y = 3/2
C. no horizontal
asymptote
Find the horizontal asymptote of:

21. Find the asymptotes of the following:

22. 6
x +
2
(a)Find the following;
- its domain,
- intercepts
- asymptotes
(b)Next, sketch its graph
ACTIVITY

23. Dengvaxia vaccine brought
fear to our fellow Filipinos.
Here in Calumpit, more than
90% of class of 2018 in
public elementary schools
had completed the three
dose vaccines.

24. a person’s bloodstream,
the concentration f of the
drug in the bloodstream x
minutes after the injection
is given by f(x) = 20x / (x +
2). Sketch the graph of f.
Identify the horizontal
asymptote of f.

25. The graph of a rational
function can be sketched by
the use of intercepts and
asymptotes.

26. Who Am I? I am a rational
function having a vertical
asymptote at the lines x = 3,
and a horizontal asymptote at
y = 1. If my only x- intercept
is -5, and my y-intercept is –
5/3, what function am I?
SEATWORK

27. 1. Find the asymptotes
of;
f(x) = 12 + 2x - 4x2
2x2 - x - 6
ASSIGNMENT: