Pre-Calculus

GRAPH OF A RASIONAL FUNCTION


A. Rasional number is number able to be expressed a/b which b=0
For example (discontinuity)
a) f(x) = (x + 2) / (x – 1)
If substitution of x=1 so f(1) = ((1) + 2) / ((1) – 1)
f(1) = i
i = imajiner
f(x) = imajiner when x=1
If substitution of x=2 so f(2) = ((2) + 2) / ((2) – 1)
f(2) = 0/1
f(x) = y, ih f(2) so x=2 and y=0
The co-ordinate is (2,0)
f(x) = (x + 2) / (x – 1) having value If x 1,
• f(x) = (x + 2) / (x – 1) discontinuity
Hp:{x| x < 1 and x > 1, x subset riil number} or can we white (negative infinity,1) and (1,positive invinity)
Example ( continuity )
b) g(x) = 1 / (x^2 +1)
The function of g(x) always having value because the dominator don’t consist of zero for x R.
If x = 1, g(1) = ½
x = 2, g(2) = 1/5
• g(x) = 1 / (x^2 + 1) continuity
Hp={x | x subset R} or can we write (positive infinity, 1 ]
Polynomial
There are two ways to get the value from polynomial function
1. Subtitute of number for the variable.
Example:
g(x) = (x^2 + x – 6) / (x – 3)
x=3, baaad! (not allowed)
 This method used direct by including value x
g(x) discontinuity if x=3 because g(x) = 0/0
2. Factor of the polynomial function
Example:
g(x) = (x^2 + x – 6) / (x – 3)
We can formulate (x^2 + x – 6) to (x-3)(x+2), so

g(x) = (x^2 + x – 6) / (x – 3)
= (x - 3).(x + 2) / (x – 3)
= (x + 2)
= x + 2
x=3, no problem!!
Domain g(x) = x subset riil number