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What is a function?
A function f is a set rule that assigns to each element x in aset A exactly one element, called f(x) in a set B

What is the independant variable and what is the dependant variable of y = f (x)
y is the dependant variable, & x independant variable

Squaring the fuction: f(x)=x^{2
a) evaluate f(3), f(√5)
b) find domain and range of f}^{}
 a) f(3)= 3^{2 }= 9, f (√5)=√5^{2}=25
 b) all real numbers f is ⎨y⎮y≥0, ⎬[0,∞)

Evaluating a Function: f(x) = 3x^{2}+ x  5 ; f(2)
 f(2) = 3(2)^{2}+ (2)  5
 = 12  2 5
 = 5

Evaluating a Function: f(x) = 2x^{2} + 3x  1
f(a)
f(a)
f(a+h)
f(a+h)  f(a) /h; h≠0
 f(a) = 2a^{2} + 3a  1
 f(a)=2(a)^{2}+3(a)1 = 2a^{2}3a1
 f(a+h) = 2(a+h)^{2} +3(a+h)  1
 = 2(a^{2}+2ah+h^{2}) +3a+3h  1
 = 2a^{2}+4ah+2h^{2}+3a+3h  1
 f(a+h)  f(a) /h
 = (2a^{2}+4ah+2h^{2}+3a+3h  1) (2a^{2}+ 3a  1)/h
 = 2a^{2}+4ah+2h^{2}+3a+3h  1 2a^{2} 3a + 1)/h
 = 4ah+2h^{2}/h
 = h(4a+2h)/h
 = 4a+2h

