Intro to TranslationHorizontal Shifts

Recall from 30SP

"k" shifts f(x) vertically up/down by k-units

"h" shifts f(x) horizontally left/right

(x - h) --> shifts right by h-units(x + h) --> shifts left by h-units

"a" stretches or compresses f(x) vertically

a>1 vertical stretch occursa<1 vertical compress occurs

Need to know some base graphs:

ex. Given the graph of f(x),

Sketch the graph of

y = f(x -1) - 3

ex. The function y = f(x) has the domain -1 x 4 and range

2 y 7. What are the domain and range of y = f(x - 5) + 1?≤ ≤

≤ ≤

State the equation for the following functions in relation to M(x)

ex. Describe the following in words:

ex. The graph of y = |x| is translated 7 units right and 6 units

up. What is the equation of the image graph?

Assignment p.168 #1, 2, 4-16