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4.3 Writing & Graphing Functions

4.3 Writing & Graphing Functions. Algebra 16,17, 18. Writing Equations. Practice. When an equation has two variables, its solutions will be all ordered pairs (x,y) that make the equation true. We can graph those solutions.

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4.3 Writing & Graphing Functions

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  1. 4.3 Writing & Graphing Functions Algebra 16,17, 18

  2. Writing Equations

  3. Practice

  4. When an equation has two variables, its solutions will be all ordered pairs (x,y) that make the equation true. • We can graph those solutions. • When we graph all solutions of an equation, that means we are graphing the equation.

  5. Recall that an equation with two variables is a relation, and it may or may not be a function. • One way to determine if a relation is a function is to graph the equation, and then use the vertical-line test.

  6. Vertical Line Test - Functions y y y y x x x x Function y y y y x x x x

  7. Vertical Line Test - Functions y y y y x x x x Function Function y y y y x x x x

  8. Vertical Line Test - Functions y y y y x x x x Function Function Not a Function y y y y x x x x

  9. Vertical Line Test - Functions y y y y x x x x Function Function Function Not a Function y y y y x x x x

  10. Vertical Line Test - Functions y y y y x x x x Function Function Function Not a Function y y y y x x x x Not a Function Not a Function Not a Function Function

  11. Graphing Functions

  12. Practice

  13. Domain & Range of Functions • Looking at the graph can help you find domain and range.

  14. Function Variables • In a function you have independent and dependent variables. • Independent variable • Usually x • Does not depend on the other • Dependent variable • Usually y • Depends on x

  15. Function Notation • If x is independent and y is dependent, the function notation for y is f(x). • You read f(x) as “f of x”. • The f is the name of the function and x is the independent variable.

  16. Writing Functions • Identify the independent and dependent variables. Write a rule using function notation.

  17. Evaluating Functions

  18. Function Notation

  19. Evaluate the function over the domain, x = -1, x = 0, x = 2.

  20. Review • How do we write an equation from a table of data? • What is another test we can use to see if a relation is a function or not? • How do we graph functions? • What are independent and dependent variables? • How do we evaluate functions?

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