Domain The x values of the ordered pair Range The y values of the ordered pair 35 Introduction to Functions x y 1 3 2 5 4 6 1 4 3 3 x y 4 2 3 8 6 1 1 9 5 6 x ID: 1045784
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1. Defn: A relation is a set of ordered pairs.Domain: The x values of the ordered pair.Range: The y values of the ordered pair.3.5 – Introduction to Functions
2. xy1325-461433xy42-3861-1956xy235738-2-587State the domain and range of each relation.3.5 – Introduction to Functions
3. Defn: A function is a relation where every x value has one and only one value of y assigned to it.xy1325-461433xy42-3861-1956xy235738-2-587functionnot a functionfunctionState whether or not the following relations could be a function or not.3.5 – Introduction to Functions
4. Functions and Equations.xy0-357-2-74533xy24-24-41639-39xy111-1424-200functionfunctionnot a functionState whether or not the following equations are functions or not.3.5 – Introduction to Functions
5. Vertical Line TestGraphs can be used to determine if a relation is a function.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.3.5 – Introduction to Functions
6. xyThe Vertical Line Testxy0-357-2-74533function3.5 – Introduction to Functions
7. xyxy24-24-41639-39The Vertical Line Testfunction3.5 – Introduction to Functions
8. xyxy111-1424-200The Vertical Line Testnot a function3.5 – Introduction to Functions
9. Find the domain and range of the function graphed to the right. Use interval notation.xyDomain:DomainRange:Range[–3, 4][–4, 2]Domain and Range from Graphs3.5 – Introduction to Functions
10. Find the domain and range of the function graphed to the right. Use interval notation.xyDomain:DomainRange:Range(– , )[– 2, )Domain and Range from Graphs3.5 – Introduction to Functions
11. Function NotationShorthand for stating that an equation is a function.Defines the independent variable (usually x) and the dependent variable (usually y).3.6 – Function Notation
12. Function notation also defines the value of x that is to be use to calculate the corresponding value of y.f(x) = 4x – 1find f(2).f(2) = 4(2) – 1f(2) = 8 – 1f(2) = 7(2, 7)g(x) = x2 – 2xfind g(–3). g(–3) = (-3)2 – 2(-3)g(–3) = 9 + 6 g(–3) = 15(–3, 15)find f(3).3.6 – Function Notation
13. Given the graph of the following function, find each function value by inspecting the graph.f(5) =7xyf(x)f(4) =3f(5) =1f(6) =6● ●●●3.6 – Function Notation
14. 3.6 – Function Notation