## 1-1 : Four ways to represent a function

Function

– function f $\rightarrow$ rule that assigns to each element x in a set D exactly one element, called f(x), in set E.

– Usually consider: D,E  sets of real numbers.

– D$\rightarrow$domain, and E$\rightarrow$range.

Representations of functions

1- verbally (words) 2- numerically (table) 3- visually (graph) 4- algebraically (formula).

Summetry

 function In algebra In geometry even f(-x)= f(x) Its graph is symmetric with respect to the y-axis Odd f(-x)= -f(x) Its graph is symmetric about the origin

Increasing and Decreasing functions

increasing:x1$<$x2 $\Leftrightarrow$f(x1$<$f(x2)

decreasing: x1$<$x2$< \Leftrightarrow$f(x1$>$f(x2)

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calculus stewart 7th