7_Intro_to_Functions

7_Intro_to_Functions

• 1.
  Functions Students willdetermine if a given equation is a function using the vertical line test and evaluate functions given member(s) of the domain.
• 2.
  | -2 IntervalNotation Algebraic Notation Graph Interval Notation x > 3 -1 ≤ x < 5 x < -2 or x ≥ 4 | 3 o | -1 | 5  o | 4 o 
• 3.
  A function isa 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.
  Domain Range XY f x 2 x 1 x 3 y 2 y 1 y 3 Mapping
• 5.
  Functions? State thedomain and range. Function Domain: {-2, 3, 5} Range: {1, -2, 7} Function Domain: {-4, 1, 6} Range: {1, -8} Not A Function
• 6.
  Determine which ofthe following relations represent functions. Not a function Function Function
• 7.
  Vertical-Line Test Ifevery vertical line intersects a given graph at no more than one point, then the graph represents a function. function not a function
• 8.
  x y Nota function. Function?
• 9.
  x y Function.
• 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.
  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.
  Modeling With FunctionsExample 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.