Pre-Calculus 40S Winter 2011 Period B: Stretches and Compressions

Good morning everyone
Im Aman....Yesterday we continued learning about Stretches and Compressions...so.I'll just do a quick review on it
RULES-
Vertical Stretches and Compressions
We say that given f(X), a>0:
y=af(X) stretches the entire graph verticaly by a factor of "a" units.
y=1/a f(X) compression the entire graph vertically by a factor of "a" units.
THE VALUE OF "X" DOES NOT CHANGE!!!!
Horizontal Stretches and Compressions
we say that given

f(x), a > 0:

y=f(ax) compress the entire graph horizontally by a factor of "a" units.
y=f(1/a x) stretches the entire graph horizontally by a factor of "a" units
THE VALUE OF "Y" DOES NOT CHANGE!!

EXAMPLE 1-

f(x)

If the original function is y = f (x), the sliding of the function horizontally to the left or right is given by the function f (x - a).

if it is positive than the graph slides to the left.
if it is negative the graph slides to the right.

example2-

y=f(x)

If the original function is y = f (x), the translation (sliding) of the function vertically upward or downward is the function f (x) + a

if it is positive the graph slides upward.
if it is negative the graph slides downward.

Horizontal Stretch or Compress
example 3

f the original function is y = f (x), the horizontal stretching or compressing of the function is the function f (ax).

if 0 < a <>, the graph is stretched horizontally by a factor
of a units.

if a > 1, the graph is compressed horizontally by a factor of a units.
if a should be negative, the horizontal compression or horizontal stretching of the graph is followed by a reflection of the graph across the y-axis.

example4-Vertical Stretch or Compress

y=f(x)

A vertical stretching is the stretching of the graph away from the x-axis.
A vertical compression is the squeezing of the graph towards the x-axis.

If the original function is y = f (x), the vertical stretching or compressing of the function is the function a f(x).