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Chapter 1: Functions

Chapter 1: Functions. Section A: Relations and Functions. Key Terms. Domain: (of a relationship) The set of possible values on the horizontal axis (x-axis) Range: The set which describes the possible y-values Relations: Any set of points on the Cartesian plane . Key Terms.

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Chapter 1: Functions

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  1. Chapter 1: Functions Section A: Relations and Functions

  2. Key Terms • Domain: (of a relationship) The set of possible values on the horizontal axis (x-axis) • Range: The set which describes the possible y-values • Relations: Any set of points on the Cartesian plane

  3. Key Terms • Equation: expresses the relation which connects the variable x and y

  4. Equation • Example: y = x + 3 and x = y² + 1 • These equation generate sets of ordered pairs

  5. Equations • There are some relationships that can’t be defined by an equation i.e. All points in the first quadrant are a relation x>0, y>0

  6. Functions • Function: is a relation in which no two different ordered pairs have the same e-coordinate • Function is a special type of relationship

  7. Testing for Functions • Algebraic Test: • If a relation is given as an equation and the substitution of any value for x results in one and only one value of y, we have a function • i.e. • y = x + 3 is a function, as for any value of x there is only one value of y • x = y² is not a function since if x = 4 then y = +2 and -2

  8. Testing for Functions • Geometric Test (“Vertical line test”) • If we draw all possible vertical lines on the graph of a relation, the relation: • Is a function, if each line cuts the graph no more than once • is not a function if one line cuts the graph more than once • See example

  9. Graphical Notes • If a graph contains a small open circle end point, the end point is not included • If a graph contains a small filled in circle end point, the end point is included • If a graph contains an arrowhead at the end, then the graph continues indefinitely in the general direction, or the shape may repeat as it has done previously

  10. Homework/Classwork • Page: 18-19 • #1-4

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