examples

Example : graph the function y=x2 over the interval [-2,2]


X=-2, y=4
X=-1, y=1
X=3/2, y=9/4 y=x2













Example : Graph y=1/x+1
X Y (x, y)
2 1/3 (2,1/3)
1 1/2 (1,1/2)
0 1 (0,1)
-2 -1 (-2, -1)












Homework: graph the function y=1/x , y=(4-x)1/2


Sums , differences , products and quotients of functions :

Like numbers, functions can be added , subtract , multiplied and divided to produce new functions.
If f and g are functions then :

(f+g) (x)= f(x)+g(x)
(f-g)(x)= f(x) –g(x)
(fg)(x)=f(x).g(x)
(f/g)(x)=f(x)/g(x) where g(x) not equals zero .
(cf)(x)= c f(x) , c= constant


Composite functions

If f(x)= , g(x)=x+1 then



(g )(x)=g( )

(f f )(x)= f(f(x))=x1/4

H.W: find f+g and f.g and their domain and ranges :

1. f(x)=x , g(x)=

2. f(x)=x+5, g(x)=x2-3 find :
f(g(0)), f(f(-5)), g(f(2))

3. find f/g and g/f and D, R , f(X)=2 , g(x)=x2+1

3. u(x)= 4x-5, v(x)=x2, f(x)=1/x find u(v(f(x))), v(u(f(x))), f(v(u(x))).