Math- Transformations of Functions
Fadi77
math_122_quiz_6.pdf
MATH 122 QUIZ 6 – Sections 2.5, 2.6, 2.8 Name _______________________________
1) Given the graph of the function f shown, consider the transformations specified by g and h .
List, in order, the sequence of transformations for each of g and h . Then very clearly graph them.
( ) ( 2) 1g x f x= − − 1 2
( ) (2 )h x f x= −
2) Determine the center and radius of the circle defined by 2 2
2 4 44x x y y+ + − = and graph the equation,
clearly labeling the center and key points. Use the graph to find the relation’s domain and range.
Center:_______________ Radius:________________
Domain:______________ Range:________________
-10 -5 5 100 -10
-5
5
10
0 x
y=f(x)
-10 -5 5 100 -10
-5
5
10
0 x
y=g(x)
-10 -5 5 100 -10
-5
5
10
0 x
y=h(x)
-10 -5 5 10 -10
-5
5
10
x
y
3) Use 1
( ) 4
f x x
= −
, ( ) 3 1g x x= + , and ( ) 3 5h x x= − to complete parts a) – e).
a) Express the domain of each function in interval notation. Show your work where work is needed.
Domain of f : Domain of g : Domain of h :
b) Find ( ) ( )f g x+ and determine its domain.
c) Evaluate ( ) (5)fg , ( ) (1)h g− , and (0) g
h
. Clearly show all of your work.
d) Find and simplify ( ) ( )f h x� and ( ) ( )g h x�
e) Evaluate ( ) (8)h g�
4) Given the two points (–10, 1) and (2, 6):
a) Find the distance between them.
b) Find the midpoint of the line segment that connects them.
