      ### UNIT 2  : FUNCTIONS

LESSON 9:  FUNCTIONS REVIEW & SUMMARY

1.  Functions: definition, notation, tests, domain and range - see lesson 1.

Def’n: A function is a relation such that for each value of x, there corresponds exactly one value of y.

Tests:

·        Vertical line test – if a vertical line cuts the graph more than once --  not a function

·        If no two ordered pairs have the same first element, then the relation is a function

·        Substitute in a value for x;  if you get more than one answer for ynot a function

Tips for finding domain:

·        Set of all first components of the ordered pairs.

·        Is there a largest value for x?  Is there a smallest value for x?

·        Are there any restrictions on x?

Tips for finding range:

·        Set of all second components of the ordered pairs.

·        Is there a largest value for y?  Is there a smallest value for y?    2.  Transformations: Example:  Describe  -2f [½ (x – 3)] – 1   relative a given function y = f(x)

·        Reflection in the x-axis

·        Vertical stretch factor 2

·        Horizontal stretch factor 2

·        Horizontal translation right 3

·        Vertical translation(shift) down 1

To graph, take points on original graph of y = f(x) and use the mapping form to determine image points  --  see Lesson 7.   3.  Inverses:      In summary, if we restrict the domain of the given parabola to that half either to the right or left of the vertex, the inverse will be a function.        