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1.2 FUNCTIONS

P.O.D. Write the slope-intercept forms of the equations of the lines through the given point (2,1) & a)Parallel & b)Perpendicular to the line 4x – 2y = 3. 1.2 FUNCTIONS. Relation - a mapping, or pairing, of input values (Domain) to output values (Range). Ex. {(1,0),(1,2),

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1.2 FUNCTIONS

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  1. P.O.D. Write the slope-intercept forms of the equations of the lines through the given point (2,1) & a)Parallel & b)Perpendicular to the line 4x – 2y = 3.

  2. 1.2 FUNCTIONS

  3. Relation- a mapping, or pairing, of input values (Domain) to output values (Range). Ex. {(1,0),(1,2), (2,1), (2,3), (3,2), (3,4)} is a relation.

  4. More examples of relations- • Your name & your student ID # • Time of day & temperature • Radius and Area of a circle

  5. Function-a type of relationship where each input is matched with exactly one output. *each ordered pair has a different x-coordinate

  6. Would these coordinates come from a function?? Ex.{(1,0),(1,1),(2,1),(2,3), (3,2), (3,4)} NOT a function.

  7. FunctionNot a Function

  8. Vertical Line Test- if any vertical line is drawn so that it intersects the graph at one and only one point then it is a graph of a function.

  9. FunctionNot a Function

  10. “y as a function of x” -Means that the variable y depends on the variable x. -y is the dependent variable and x is the independent variable.

  11. Testing for functions Algebraically 1) Solve the eq. for y 2) Make sure that for any given value of x there will only be only one value for y.

  12. Ex.Determine whether the equation represents y as a function of x: 1) x2 + y2 = 8 2) x = y3 - 5

  13. FUNCTION NOTATION:*Functions are named by using a single letter: f, g, h, F, G, Ф, etc. Ex. f(x) “the value of function f at x” or “f of x”

  14. *The ordered pair for a function is (x, f(x))“f(x)” is basically the same as “y”, except “y” can be used in an equation that is not a function, unlike “f(x)”

  15. EVALUATING FUNCTIONS:Let f(x) = 10 – 3x2 find :a. f(2)b. f(-4)c. f(x – 1) Evaluating is simply substituting in a value or expression for x.

  16. Piecewise-Defined Function A function defined by two or more equations over a specified domain

  17. Absolute Value Function as a Piecewise-Defined Function

  18. More examples of Piecewise Functions

  19. Graph then evaluate the following:a. f(2) b. f(-4) c. f(5)

  20. Implied Domains: The Domain of each function is all real numbers for which the function is defined. It describes all possible “inputs” of the function.

  21. Evened-Root Functions Ex. 1 Ex. 2 Ex. 3

  22. Rational Functions Ex. 1 Ex. 2

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