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Functions

Functions. Section 1.4. Relation. The value of one variable is related to the value of a second variable A correspondence between two sets

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Functions

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  1. Functions Section 1.4

  2. Relation • The value of one variable is related to the value of a second variable • A correspondence between two sets • If x and y are two elements in these sets and if a relation exists between x and y, then xcorresponds to y, or ydepends onx, written xy • x is the input to the relation and y is the output of the relation

  3. Ways to Express Relations • Equations • Graphs • Mapping • Use a set of inputs and draw arrows to the corresponding element in the set of outputs • See page 31

  4. Function • A relation that associates with each element of a domain exactly one element in the range (called the value or image) • Denoted by letters such as f, F, g, G, etc. • To determine if a relation is a function, solve equation for y • More than one solution for y: not a function • Otherwise it’s a function

  5. Page 43 15. 19. 33.

  6. Find the Value of a Function • f(x) • f of x • f at x • The value of f at the number x • x is the independent variable (argument) • y is the dependent variable

  7. For the function f defined byf(x) = x2 + 4x, evaluate (A) f(3) (B) f(x) + f(3) (C) f(-x)

  8. For the function f defined byf(x) = x2 + 4x, evaluate (D) -f(x) (E) f(x + 3)

  9. For the function f defined byf(x) = x2 + 4x, evaluate (F)

  10. is called the difference quotientof f

  11. When a function is defined by an equation in x and y, the function f is given implicitly.If it’s possible to solve the equation for y in terms of x, write y = f(x), which means the function is given explicitly.

  12. Pages 43-44 (24-46 even)

  13. Find the Domain of a Function • The domain of f is the largest set of real numbers for which the value f(x) is a real number. • If x is in the domain of a function, f is defined at x, or f(x) exists. • If x isn’t in the domain of a function,f is not defined at x, or f(x) does not exist.

  14. Sum of two functions Difference of two functions

  15. Product of two functions Quotientof two functions

  16. Page 44 61.

  17. page 44(48, 52, 56, 58, 62-70 even, 73-78)============================pages 44-45(50, 54, 60, 80, 82, 84, 86, 87, 89)

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