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Defn: A relation is a set of ordered pairs.

3.5 – Introduction to Functions. Defn: A relation is a set of ordered pairs. Domain: The values of the 1 st component of the ordered pair. Range: The values of the 2nd component of the ordered pair. 3.5 – Introduction to Functions. State the domain and range of each relation.

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Defn: A relation is a set of ordered pairs.

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  1. 3.5 – Introduction to Functions Defn: A relation is a set of ordered pairs. Domain: The values of the 1st component of the ordered pair. Range: The values of the 2nd component of the ordered pair.

  2. 3.5 – Introduction to Functions State the domain and range of each relation.

  3. 3.5 – Introduction to Functions Defn: A function is a relation where every x value has one and only one value of y assigned to it. State whether or not the following relations could be a function or not. function function not a function

  4. 3.5 – Introduction to Functions Functions and Equations. State whether or not the following equations are functions or not. function not a function function

  5. 3.5 – Introduction to Functions Graphs can be used to determine if a relation is a function. Vertical Line Test If a vertical line can be drawn so that it intersects a graph of an equation more than once, then the equation is not a function.

  6. 3.5 – Introduction to Functions The Vertical Line Test y function x

  7. 3.5 – Introduction to Functions The Vertical Line Test y function x

  8. 3.5 – Introduction to Functions The Vertical Line Test y not a function x

  9. 3.5 – Introduction to Functions y x Domain and Range from Graphs Find the domain and range of the function graphed to the right. Use interval notation. Domain Range Domain: [–3, 4] Range: [–4, 2]

  10. 3.5 – Introduction to Functions y x Domain and Range from Graphs Find the domain and range of the function graphed to the right. Use interval notation. Range Domain: (– , ) Range: [– 2, ) Domain

  11. 3.6 – Function Notation Function Notation Shorthand for stating that an equation is a function. Defines the independent variable (usually x) and the dependent variable (usually y).

  12. 3.6 – Function Notation Function notation also defines the value of x that is to be use to calculate the corresponding value of y. g(x) = x2 – 2x find g(–3). f(x) = 4x – 1 find f(2). find f(3). f(2) = 4(2) – 1 g(–3) = (-3)2 – 2(-3) f(2) = 8 – 1 g(–3) = 9 + 6 f(2) = 7 g(–3) = 15 (2, 7) (–3, 15)

  13. 3.6 – Function Notation y f(x) x Given the graph of the following function, find each function value by inspecting the graph. ● ● 7 f(5) = ● 3 f(4) = 1 f(5) = 6 f(6) = ●

  14. 3.6 – Function Notation

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