Core 3 Functions

Core 3 Functions

1. Definitions

   • Domain- x values/independent variable Range- y values/dependent variable
   • One-One relationship
     • Each y value has only one x value
   • Many-One relationship
     • Many x values with only one y value
   • One-Many relationship
     • One x value for many y values
   • Many-Many relationship
     • Many x values for many y values
   • Can only be a function if the relationship is One-One or Many-One

2. Composite functions

   • When 2 or more functions are combined. The output of the first becomes the input of the second
   • fg(x) - apply g first then, put the answer into the function of f(x)
   • Only if range of the second is contained within the first

3. Inverse functions

   • f^(-1)(x)
   • If f(x) = f^(-1)(x) Then the function is self-inverse
   • The range of f(x) is the domain of f^(-1)(x) and vica versa
   • The graphs are reflections of each other
   • Re-arrange f(x) for x in terms of y to find the inverse

4. Even and odd functions

   • Even function is where f(x) = f(-x)
     • The graph is symmetrical about the y axis
   • Odd function is where f(x) = -f(-x)
     • The graph has a 180 degree rotational symmetry

5. Modulus function

   • |x| means the magnitude of x i.e. |6| = 6
   • y = |f(x)|
   • y = f(|x|)
   • If both sides of an equation involving modulus signs is positive, square both sides. Otherwise find the points of intersection

6. Transformations of graphs

   • Check whether the answer should be in radians or degrees

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