Transformations
Write transformations in the following order
•
Shifts left/right
•
Shrinks/stretches
•
Reflections
•
Up/down
Shifts:
•
•
•
•
f(x + C)
f(x - C)
f(x)+c
f(x)-C
Shifts left: horizontal translation left C units
Shifts right: horizontal translatio~n right C units
Shifts up: vertical translation up C units
Shifts down: vertical translation down C units
Reflections:
•
-f(x) reflection in the X-axis (notice the negative is outside the function.)
•
f( -x) reflection in the V-axis (notice the negative is inside the function)
Vertical shrinks/stretches
Horizontal shrinks/stretches
f(f)k
af(x)
If a >1 then it is a vertical stretch by a factor of a
If b>l then it is a horizontal stretch by a factor of b .
If 0 < a < 1 then it is a vertical shrink by a factor of a
If 0 < b < 1 then it is a horizontal shrink by a factor of b
Describe the transformation on the parent graph [ex) =
1. [ex)
= ..Jx
2. gex)
= {X + 2
3.. hex)
= ...:...Jx + 1
4. [ex)
= 2{X-4
5. [ex)
=...;sx
6. [(x)
= =-.J
3
7. [ex)
= J~X+4
8. [ex)
= ..J2x + 1 -
{X
3
x
(.-
5
..
Simplify the expressions by using the properties of rational exponents
q, (\\*.
\\5/~J'/3
\U.
~::
II,
C:~JL
J .2-.
Use the properties of radicals to simplify the radicals
1(P)
~~ 0 _
\Ii
~. /003
_~
\~ ')
~JO ,t-~
-
L-J~ (q.-- J.g)
Solve for the real zeros. Round to the nearest hundredths when appropriate.
\~)
.-t XS_;< -=- _\\
j2o,
-3Cx -,-\)fe ~~ ==- -38