1 10 X 8/24 8/ X

1 X 8/30/10 8/ X

Section 1.1 Four Ways to Represent a Function SWBAT –Represent functions using “The DANG” –Evaluate the Difference Quotient –Put the “Fun” in Piecewise function

Representations of Functions Functions can be represented in four ways: –Descriptive (that is, by a description in words) –Algebraically (by an explicit formula) –Numerically (by a table of values) –Graphically ( visual) It is often useful to convert from one representation to another, where possible.

Slope formula or But there is another way...

f(x+h) f(x)

Difference Quotient Example: if f(x)= 4x 2 -2x+7 and h≠0, evaluate the difference quotient.

Piecewise Defined Functions Sometimes functions are defined by different formulas in different parts of their domains. Example: If Find f(0), f(1), and f(2) (might be helpful to look at the graph of f(x))

Piecewise (cont’d) To graph f, note that… –for x ≤ 1, the graph of f must coincide with the line y = 1 – x, whereas –for x > 1, the graph must coincide with the parabola y = x 2. Here is the graph:

ASSIGNMENT 3 What is a limit WS