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Lessons 2.1, 2.3, 2.4, and 2.6

Lessons 2.1, 2.3, 2.4, and 2.6. Functions Properties of Functions Library of Functions Operations on Functions. Relations: Any correspondence between two sets (x,y). Functions: Is a relations that associates with each element of x exactly one element of y. Vertical Line Test.

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Lessons 2.1, 2.3, 2.4, and 2.6

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  1. Lessons 2.1, 2.3, 2.4, and 2.6 Functions Properties of Functions Library of Functions Operations on Functions

  2. Relations: Any correspondence between two sets (x,y) Functions: Is a relations that associates with each element of x exactly one element of y. Vertical Line Test Relations and Functions

  3. Key Words Related to Functions • Domain and Range • Value: given x what is the value of y? • One-to-one correspondence • Independent and Dependent Variable • Explicit and Implicit Form • Even or Odd Functions

  4. Obtaining Information from the Graph of a Function • Domain and Range • x and y-intercepts • Symmetry – Even or Odd • Increasing, decreasing or constant • Local Maxima, Local Minima

  5. Function Notation • y = f(x) • f is a symbol for the function • x is the independent variable • y is the dependent variable • f(x) is the value of the function (y) at x

  6. Library of Functions • Linear function Constant function Identity function • Square function • Cube function • Square Root function • Reciprocal function • Absolute Value Function • Greatest-Integer Function (A only)

  7. Piecewise Functions functions defined by more than one equation Ex. The absolute value function is an example of a piecewise function.

  8. Operations on Functions • Functions like numbers can be added, subtracted, multiplied, and divided. • f + g, f – g, fg, f/g • The domain of f +g, f – g, and fg consists of all numbers x in the domain of both f and g. (intersection of two domains) • The domain of f/g consists of all numbers x in the domain of both f and g for which g(x) is not equal to zero.

  9. Composition of Functions • Notation: f (g (x)) or f o g, where f is the outer function and g is the inner function. • The domain of a composition is the set of all numbers x in the domain of the inner function that satisfy the composition. • Decomposition: the process by which you find the components of a composite function.

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