7_Intro_to_Functions

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7_Intro_to_Functions

  1. 1. Functions Students will determine if a given equation is a function using the vertical line test and evaluate functions given member(s) of the domain.
  2. 2. | -2 Interval Notation Algebraic Notation Graph Interval Notation x > 3 -1 ≤ x < 5 x < -2 or x ≥ 4 | 3 o | -1 | 5  o | 4 o 
  3. 3. A function is a relationship or correspondence between two sets of numbers, in which each member of the first set (called the domain ) corresponds to one an only one member of the second set (called the range ). Function, Domain, and Range
  4. 4. Domain Range X Y f x 2 x 1 x 3 y 2 y 1 y 3 Mapping
  5. 5. Functions? State the domain and range. Function Domain: {-2, 3, 5} Range: {1, -2, 7} Function Domain: {-4, 1, 6} Range: {1, -8} Not A Function
  6. 6. Determine which of the following relations represent functions. Not a function Function Function
  7. 7. Vertical-Line Test If every vertical line intersects a given graph at no more than one point, then the graph represents a function. function not a function
  8. 8. x y Not a function. Function?
  9. 9. x y Function.
  10. 10. Function Notation f (x) f is the name of the function x is the variable into which we substitute values or other expressions x is called the independent variable and f ( x ) is the dependent variable . Does Not Mean f times x. Read: “f of x”
  11. 11. Evaluating Functions Let f ( x )=2 x – 3 and g ( m ) = m 2 – 2 m + 1. Determine: a.) f (-3) c.) f ( 1/2 ) b.) g (-2) d.) g ( a + 1)
  12. 12. Modeling With Functions Example 1 Express the surface area of a cube as a function of its volume. Example 2 A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the window is 30 ft, express the area A of the window as a function of the width x of the window.

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