College Algebra, 2013a

1.7 Transformations 139
shift right 1 unit
−−−−−−−−−−−−→
add 1 to each x-coordinate
y = g 2 (x) =−x 2 − 2 y = g 3 (x) =g 2 (x − 1) = −x 2 +2x − 3
horizontal stretch by a factor of 2
−−−−−−−−−−−−−−−−−→
multiply each x-coordinate by 2
y = g 3 (x) =−x 2 +2x − 3 y = g(x) =g 3
( 1
2 x) = − 1 4 x2 + x − 3
We have kept the viewing window the same in all of the graphs above. This had the undesirable
consequence of making the last graph look ‘incomplete’ in that we cannot see the original shape
of f(x) =x 2 . Altering the viewing window results in a more complete graph of the transformed
function as seen below.
y = g(x)
This example brings our first chapter to a close. In the chapters which lie ahead, be on the lookout
for the concepts developed here to resurface as we study different families of functions.