Functions and Graphs

Functions and Graphs

1. Domain- x values

   • Largest set of real numbers for which f(x) exists
     • ie. dom f={ x ϵ ℝ: x≠1, x≠2}
   • Range of inverse= dom of f(x)

2. Range- y values

   • y=f(x)
     • domain of inverse = range of f(x)

3. FUNCTION (f)

   • Output f(x) (y)
   • Input (x)

4. Cannot divide by zero

5. Can't take square root of negative

6. Expressed explicitly or implicitly

   • Implicit- i.e. y= xy+3x+4y-7
   • Explicit- i.e. y= x^2

7. Graph of a function - curve of straight line

   • Range can be determined

8. Vertical test

   • If line crosses 1> points
     • Not a function

9. Combining two functions- replace x with function

   • Composition
     • (fog)(x)= f(g(x))

10. Reflecting, shifting and stretching

11. Inverse function- undoes the original function

12. Horizontal test

    • line crosses 1> point
      • No inverse

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