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Mastering Calculus: Functions, Formulas, and Representations

Learn to represent functions in Algebraic, Graphical, Numerical, and Descriptive ways. Understand the Difference Quotient and Piecewise Defined Functions. Get ready for Assignment 3 on Limits.

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Mastering Calculus: Functions, Formulas, and Representations

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  1. Welcome to another new day of: Calculus Get out your assignment

  2. 1 2 2 X X 10 10 8/24 8/25

  3. 1 2 X X 10 10 8/30/10 8/31

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

  5. 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.

  6. Slope formula or But there is another way . . .

  7. f(x+h) f(x)

  8. Difference Quotient Example: if f(x)= 4x2-2x+7 and h≠0, evaluate the difference quotient.

  9. 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))

  10. 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 = x2 . • Here is the graph:

  11. ASSIGNMENT 3 • What is a limit WS

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