MATH 100 DR. MCLOUGHLIN'S HANDY DANDY SYSTEMATIC GRAPHING GUIDE PART II

Transcription

1 Dr. McLoughlin s Handy Dandy Graphing Guide Part II, page MATH 00 DR. MCLOUGHLIN'S HANDY DANDY SYSTEMATIC GRAPHING GUIDE PART II Here we discuss basic graphing techniques of functions from Part I. y = A f(b(x C)) + D A B C D stretches or contracts and flips along the y axis stretches or contracts and flips along the x axis shifts left or right along the x axis shifts down or up along the y axis Example : y = (x ) Note the domain is R and the codomain is R. First graph y = x notice the point (0, 0) then y = (x ) which shifts the graph right (0, 0) moves to (, 0) then y = (x ) which stretches and finally y = (x ) which shifts the graph with respect to y the graph down (, 0) doesn t move (, 0) moves to (, -) Now the domain is R, the codomain is R, and the range is [-, )

2 Dr. McLoughlin s Handy Dandy Graphing Guide Part II, page Example : y = x+ +π Note the domain is R and the codomain is R First graph y = x then y = -x which reflects it across the y-axis notice the point (0, 0) (doesn t change anything including the point (0, 0)) then y = x+ which shifts then y = x+ which contracts the graph the graph right one with respect to the y-axis ( squeezes it down some ) (0, 0) moves to (, 0) the point (, 0) doesn t change and finally, y = x+ +π which shifts the graph up π. notice the point (, 0) moves up to (, π). Note the domain is R, the codomain is R, and the range is [π, )

3 Dr. McLoughlin s Handy Dandy Graphing Guide Part II, page Example : - y = x + Note the domain is [-, ) and the codomain is R First graph y = x (the domain is [0, )) then y = x+ (the domain is now [-, )) notice the point (0, 0) which shifts it left and (0, 0) moves to (-, 0) then y = x+ which reflects - then y = x + which stretches the graph it across the x-axis with respect to the y-axis (-, 0) doesn t move (-, 0) doesn t move Note the domain is [-, ), the codomain is R, and the range is (, 0].

4 Dr. McLoughlin s Handy Dandy Graphing Guide Part II, page Example : y = (x ) + Note the domain is (, ) (, ) and the codomain is R First graph y = x = then y = (x ) x (the domain is (, 0) (0, )) (the domain is now (, ) (, )) notice there isn t the point (0, 0) which shifts it right on this graph - there is a vertical asymptote x = 0 the vert. asy. x = 0 moves to x =. Now graph y = (x ) and, finally, graph y = (x ) + which stretches it with respect which shifts it up to the y-axis (hardly noticeable) so the horizontal asymptote y = 0 the vert. asy. is x = shits up to y = Note the domain is (, ) (, ), the codomain is R, and the range is (, ).

5 Dr. McLoughlin s Handy Dandy Graphing Guide Part II, page Example : y = (x ) + Note the domain is R and the codomain is R First graph y = x then y = (x ) notice the point (0, 0) which shifts it right (0, 0) moves to (, 0) Now graph y = (x ) and, finally, graph y = (x ) + which stretches it with respect which shifts it up to the y-axis (, 0) moves to (, ) (, 0) doesn t move Note the domain is R, the codomain is R, and the range is R.

6 Dr. McLoughlin s Handy Dandy Graphing Guide Part II, page 6 Exercises:. y = (x ) +, track the point (0, 0),. y = (x+ ) + 6, track the point (0, 0),. y = x +, track the point (0, 0),. y = x, track the point (0, 0),. y = (x+ ) + track vertical and horizontal asymptotes, 6. y = (x+ ) +, track the point (0, 0), 7. y = (x+ ) +, track the point (0, 0), 8. y = (x ) +, track the point (0, 0), 9. y = (x+ ), track the point (0, 0), End, last revised 9 October 00.