A fraction of polynomial functions

1. GENERAL MATHEMATICS
Rational Function

2. RATIONAL FUNCTION

3. RATIONAL FUNCTION

4. REPRESENTING REAL-LIFE SITUATIONS USING
RATIONAL FUNCTIONS

5. REPRESENTING REAL-LIFE SITUATIONS USING
RATIONAL FUNCTIONS
Solution:

6. REPRESENTING REAL-LIFE SITUATIONS USING
RATIONAL FUNCTIONS
material required.

7. RATIONAL FUNCTIONS, EQUATIONS AND
INEQUALITIES

8. RATIONAL FUNCTIONS, EQUATIONS AND
INEQUALITIES

9. EVALUATING RATIONAL FUNCTION
1. Find R(2) for the rational function.
R x =
2𝑥+3
3𝑥2−2
2. Find R(-2) for the rational function.
R x =
𝑥2+3
2𝑥+2

10. EVALUATING RATIONAL FUNCTION
3. A local electric fan manufacturer spent
P10M to develop a powerful 3-speed
electronic fan to be sold at P950. If the cost of
producing each electric fan is P600,
determine the rational function that will give
the average cost of producing x electric fans.
Determine the average cost per electric fan
for producing a) 50,000 electric fans; b)
2,000,000 electric fans.

11. EVALUATING RATIONAL FUNCTION
4. A travel agent offers a tour package
covering airplane tickets, shuttle
transportation and hotel accommodations. It
costs the agent P500,000 plus P6,000 per
person to accommodate the airfares. Find the
a rational function for the average price per
person for the airfares. How much is the
average cost peer person if 50 persons buy
the tour package?

12. SEATWORK
 The manufacturer of wristwatches spent P10M to
develop and produce a plastic wristwatch for
teenagers to be sold at P500 each. If the cost of
producing each wristwatch is P360, determine the
rational function that will yield the average cost of
producing x wristwatches. Determine the average
cost per wristwatch for producing a) 40,000
wristwatches, and b) 10,000,000 wristwatches.

13. GRAPH OF RATIONAL FUNCTIONS
Sketch the graphs of rational functions
by;
 Finding and plotting the horizontal and
vertical asymptotes,
 Finding and plotting the symmetry
 Finding and plotting the ordered pair
values for x and y in the Cartesian
Plane.

14. GRAPH OF RATIONAL FUNCTIONS
A. Sketch the graph of the rational function.
a) 1/x b) 1/ x2 c) 𝑓 𝑥 =
𝑥 − 2
𝑥 + 5
Solution:
 Find the vertical and horizontal asymptotes
 Determine the symmetry
 Prepare a table of ordered pair values for x and y.

15. Vertical asymptote
-let p(x)/q(x) and solve for q(x) =0.
 Horizontal asymptote
-let p(y)/q(y) and solve for q(y) = 0.
Determine the symmetry
Odd function if it is symmetric to the origin.
Even Function if it is symmetric to the y-axis.

16.  Sketch the graph of f(x) = (3x-1) / (x2 – 9)
F(x) = (x+4)/(x-2)