## Transcribed Text

(1 point) The graph of y = x is given below:
Find a fonnula for each of the transformatio ns whose graphs are given below.
Recall that absoluta value is enterad as abs.
a)
y =
b)
y =
••
(1 polnt) FORMULAF ROMS QRTG RAPH
The graph shown Is a shlft, also callad a translatlon, of y
a= ±lor ±2.
- -,'- - -,'- - ,' - - ,' - - 'r - - 'r - -,'- - -,'- - ,-' - ·
·1 O
1 •
L .. .,1,. • .,1
.,. .,
-,- .. , .. - '1 - - " - - .. - - I" - .. , .. - .. , .. - "1 - - '
-4
The graph Is y
r 2 ' ' ' ' .... • .... L .... • ....
'' '' '' ' • • • •
' ' 1' 'r
' i
o ,'
. -_, - .. --~ ----- - -.. _,_ -
' ' ' ' ' 1 1 1 1 1 --~--,--r-,--,- --,-- - - r' - -,'- -
... ~ .... i .... L .. J .... 1 ........ ~ .... L .. J .... 1 .... 1 ....
' ---·--·--~-4--·----·--~-4--·--~-
---,'1 -- --,1' - ',1 -------,--,'1 11 - t, --,-'1 -,-1!-
-1 2
Find the formula tor f.
f (x) =
±Jax, where
- - ~- - _,_ - _,_ - -~ - -
' ' ' ' - - .l. - - -' - - .J_ - _,_ - _,_ - -L - - '- - -
' '
- - .1 - - .J - - J_ - -'- - -'- - -L- - L - -
1 1 __ ·- __ , ___ , __ - ·-
' 1 t 1 1
' 1 1 t 1 1
- - , - - -¡ - - ,- - -,- - -,- -
'
' ' - - "T - - ., - - ..,- - -,- - -,
'
8
- - ~- - _,_ - _,_ - -~ - -
' ' ' ' - - .l. - - -' - - .J_ - _,_ - _,_ - -L - - '- - -
' '
- - .1 - - .J - - J_ - -'- - -'- - -L- - L - - ' ' 1 , __ • ___ , ___ , ___ • __ ,
1 1 t 1 1 t 1
' ' 1 1 t 1 1 ' 1
- - -¡ - - -¡ - - ,- - -,- - -,- - -, - - ¡- - -
t' 1 1 I
- - -r - - , - - -.- - -,- - -,- - -r- - r- - -
1 1 1 1 1
- - -r - - ., - - ..,- - -,- - -,- - -r - - r- - -
-8
~--.J __ J ' ___ , ___ , ___ 'L --L- '
_, - - _,_ - 1
' ' ' '
-'---'---
'' '' I t I I t
-¡ - - -,- - -,- - -,- - - ' -
' ' ' -,' - - -,1- - - r' - - r' -
-, - - - ,- - - r- - - r -
.l.---'--~---·---·---~--'-- ~--.J __ J ' __ J ' ___ , ___ 'L --L- '
' < 1 _, ___ • __ 1 _, ___ .___
1 I t 1 ' ' '' '' 1 I ' 1 I I
-¡ - - -¡ - - -,- - -,- - -,- - - • -
' ' ~--,--,--~--' -,---r, --r- 1 ' •
---r---,--,--' -,---,---r---r-
- 1
- 1
- 1
- 1
- 1
- 1
- 1
The domain of g( x) is of the form [ a, b], where a is and bis
The ranga of g ( x) Is of the form [ e, d], where e Is and d Is
Enter the letter of the graph which corresponds to each new function defined below:
1. g(x - 2) + 2 is
2. g(2x) is
3. 2 + g(-x) is - 4. g(x + 2) - 2 is
A B e D
{V\
E F G H
(1 point) The graph of y = f (X) is given below:
2.1
A(• ,O) CI ,O) x
On a piece of papar sketch the graph of y = f ( X - 5) and determine the new
coordi nates of points A, B and c.
A=
B=
C=
On a piece of papar sketch the graph of y = - f ( x) + 2 and determine the new
coordi nates of points A, B and c.
A=
B=
C=
(1 point) The graph of y = f (X) is given below:
y
B 21
A(· ,O) C( ,O) X
On a piece of papar sket ch the graph of y = f (!X) and determine the new
coord inates of points A, B and c.
A (
B(
C (
)
)
)
(1 polnt) The graph of y = f ( x) is given below:
2.1
A(-1,0) C( ,O) X
On a piece of paper sketch the graph of y = -4 f ( 6x) and determine the new
coordlnates of polnts A, B and C.
A ( ---~ ~--- )
B ( )
C ( )
(1 point) Given f (X) = 1 X 1, after performing the following transformations: shift to
the left 14 units, shrirnk vertically by a factor of / 1, and shift downward 65 units , the
new function g (X) =
Use abs(x) for IX1-
(1 point) The graph of y = x3 - 12x2 is given below:
Find a tonn ula tor the transfonnation whose graph is given below.
y=
(1 point) The graph of y = f (X) is given below:
y
B 21
A(• ,O) C( ,O) X
On a piece of papar sketch the graph of y = f ( X - 2) and determine the new
coordi nates of points A, B and c.
A=
B=
C=
On a piece of papar sketch the graph of y = - f (X) - 1 and determine the new
coordi nates of points A, B and c.
A=
B=
C=
e o
E
8
-4
For each equatlo n, enter the letter of the corresponding graph.
y= J(x - 4)
y= -f (x + 4)
y = 2f (x + 6)
y = J(x) + 3
y = ~f(x)
(1 polnt) The graph of J.J
.
'
x2 Is
-5
lven below :
.
-. -
'
.
.
' '
.
'
.' ..- - - - .' .- - - -
. ' •
.'
Find a formula for the transformation whose graph is given below .
-.-----.-----.-----.-----
'
-.-----.-----.-----.-----
'
-.-----.-----.-----.-----
'
e ---.-----.-----.-----.-----
'
-.-----.-----.-----.-----
'
-.-----.-----.-----.-----
'
-.-----.-----.-----.-----
'
-.-----.-----.-----.-----
'
-5
y
(1p olnt)C onsldethre f unctlons (1 polntC) onsldethre f uncllons
f(x) = - 5x + 9,g(x) = 8x + 1 f(x) = 3X,g(x) = x3
Determitnhee f ollowlngc ompollslons off unctlonsD: etermitnhee f ollowlncgo mpollslonso ff unclotns:
(fof)(x)= (fof)(x)=
(fo g)(x) = (fo g)(x) =
(g o f)(x) = (g o f)(x) =
(g o g)(x) = (g o g)(x) =
1
(1 polnt) Let f (X) = x 2 + 5, g (X) = -- , and h( X) = v'2x . Flnd a x- 2
formula for
g(f(h(x))) = (......_1 ____ ____,]
(1 point) Consider the function g (X) representad by the table below:
X -6 -4 -2 0 2 4 f
g(x) o 6 -64- 2 -42
Comp lete the tab le of values for the INVERSE, g- L x , In the tab le below:
~ 4 -2 O 2 4 6
-2
(1 point) Decompose the function below into u ( v (X)). In each part, basad on the
tunct ion v( x) given, tind the correspond ing u( x) needed to decompose the
tunct ion.
3 +x2
y = 8 + x 2
(a)v(x) = x2,u(x) =
(b) v (x) = x2 + 3, u(x) =
(1 point) ldentify the function f (X) if
k(x) = (J (x))4 = cos4 (6x).
f (x) =
(1 point) ldentify the funct ion f ( x) if
j(x) = ,/J[zj = J e (x2 +1)_
f( x) =
(1 point) Use graph below to calc ulate the following:
(a) f(f(2)) =
(b) g(g(2)) =
(e) f(g(l)) =
(d) g(f(l)) =
Í (IC) •
•
(1 point) Use the table of values for the functions p( X) and q( X) below to comp lete
the tables for the compos ite functions defined in parts (a) and (b):
X 012345
p(x) 2 1 053 4
q( x) 52340 1
(a) comp lete the table of values torth e composite funct ion r( x) = p(q (x )) at
X = 0, 1,2, 3,4, 5
o 1 2 3 4 5
(b) Complete the table of values for the compos ite function s( X) = q(p( X)) at
X = 0, 1,2, 3,4, 5.
o 1 2 3 4 5
(1 point) Decompose the functio n below into u ( v ( x) ). In each part, basad on the
functlon v( x) glven, flnd the correspondlng u( x) needed to decompose the
function.
(a)v(:i;) = x5, u(x) =
(b) v(x) = x5 + 5, u(x) =
5 +x5
y=
8 +x 5
(1 point) (a) Use the tab le of values for f (X) and the graph given for g (X) to
calculate each of the following:
Qf(g(5)) =
ii)g(J(5)) = -=i
iii) f (f(O)) =
ivJ g(g(O)) =
(b)g(g(x)) = l whenx =
5
4
3
X 012345
J(x) 34052 1
---"--------J--------'---'- ----
g(x)
- - - - - -1- - - - - - - - - _,_ - - - - - - - 4 - - - - - - - J - - - - - - - _,_ - - - 1 1 1
1 2 3 4
'
(1 polnt) Suppose J(x) = -:i; 2 + 9x - 18.
(a) For which values of X is the fu nction f (X) positiva? Enter your answer using
lnequallt les.
help (lnequallt ies)
(a) For which values of X is the fu nction f (X) negativa? Enter your answer using
lnequallt les.
help (lnequallties)
(1 point) The concentr ation of a drug t seconds aft er injecti on is given by
C(t) = 9t + 1
5t2 + 3
Graph this funct ion on your calculator.
Estímate the time at which the concentrat ion is highest (your answer needs to be
correct to at least one place past the dec imal point):
Maximum is at t =