Wetzel

Math 110

2.5 – Properties of Graphs

Symmetry –

            with respect to the y-axis –       x = -x

            with respect to the x-axis –       y = -y

            with respect to the origin –        x = -x   and   y = -y

Translations –

            Given the basis quadratic function, 

            k:         vertical shift where        

                        what will  do?

            h:         horizontal shift where

                        what will   do?

            a:

                        x-axis reflection:    (a is negative where

                        y-axis reflection:  (x is negated in the function)

                        vertical stretching:         where a > 1

                                    (graph gets narrower)

                        vertical shrinking:          where 0 < a < 1

                                    (graph gets wider)

Ex.:  Sketch the following graphs.

1.)                                            2.) 

Other functions to know–

            1.) 

            2.) 

            3.) 

            4.) 

HOMEWORK:    p.240: #1, 7-17odd, 23, 25, 43, 45, 59, 67, 69