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Section 1.3 Functions

Section 1.3 Functions. Objective: To evaluate functions and find their domains To evaluate difference quotients. p. 141 #1, 5, 6, 15, 18, 31, 34, 37. Assignment. Function = set of ordered pairs A mapping from one set to another. y. x. (-2, 4) (2, 4) (1, 1) (-1, 1) (0, 0). 4 4 1

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Section 1.3 Functions

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  1. Section 1.3 Functions Objective: To evaluate functions and find their domains To evaluate difference quotients.

  2. p. 141 • #1, 5, 6, 15, 18, 31, 34, 37 Assignment

  3. Function = set of ordered pairs • A mapping from one set to another y x (-2, 4) (2, 4) (1, 1) (-1, 1) (0, 0) 4 4 1 1 0 -2 2 1 -1 0 What is this function? This is pretty functional

  4. Values from the independent variable (x) cannot be mapped to two or more dependent variables (y) (0, 1) (0, -2) Fails, think about the vertical line test. What is NOT a function?

  5. Bulls Heat Knicks Magic Eastern conference Which are functions?

  6. Name that Function

  7. Given an equation • Solve for y • Determine if each x value will have at most one y value. Solve Algebraically

  8. Solve Algebraically

  9. Function Notation

  10. What do we know: • “y =“ typically can be made into a graph • Our change: • Think about a graph not in terms of x -> y, but instead as x -> f(x) • Since we say that y is a function of x , we can replace y with f(x) making it “f(x) =“ X f f(x) X f Y 2 4 6 2 4 6 1 2 3 1 2 3 Functions, functions, functions!!!

  11. Iff(x) = x2 – 4x, find the following. a) • b) • c) f(x+ h) = • Remember: • y = f(x). • f is the name of the function, not another variable.

  12. Domain of a function

  13. p. 143 # 51, 54, 55, 63, 65, 71, 74

  14. Domain of a function: • all x such that the matching y is a real number. • consider only three situations • Polynomials  domain is (-, ). • 3x, , • Fractions  cannot have any number in the domain that makes the denominator zero. • Radicals  if the index is even, then the radicand must be nonnegative.

  15. Domain of a function: • Polynomials  domain is (-, ). • f(x) = x3 + 3x + 1 • This is a polynomial, so the domain is (-, ). • Fractions  cannot have any number in the domain that makes the denominator zero since that would make it undefined. • x + 2  0, so the domain is (-, -2)  (-2, ) • Radicals  if the index is even, then the radicand must be nonnegative. 5 – x 0, so the domain is (–, 5]

  16. What is the domain of each function?

  17. (- ∞, -3) U (-3, 7) U (7, ∞) • (- ∞, 8] • [-3, 2) U (2, ∞)

  18. Finds the slope of a line between two points on a function x tells you where you are looking at the function because different parts will have different slopes h = distance between the two points http://media.lanecc.edu/users/gettyst/Geogebra/difference_quotient.html Difference Quotient

  19. If It’s time to teach you Calculus

  20. Application

  21. Pre-read section 1.4 • On a sheet of loose-leaf paper, take notes on what you believe is important to the section • Try to think about what material will be important to the objectives in the book • Will be an assessment for me to see how well you read a textbook to see what we can work on together Assignment

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