Math
169
–
01:
Test
#2
(Chapter
2)
100
Name:
Show
as
much
work
as
possible
to
receive
full
credit.
Correct
answers
with
no
work
may
not
necessarily
receive
full
credit.
€
1.
Give
the
equation
(in
slope­intercept
form)
of
the
line
with
given
properties:
(7
points
each)
(a)
passes
through
the
points
(3,
10)
and
(–1,
2)
(b)
passes
through
the
point
(4,
–2)
and
is
perpendicular
to
the
line
4x −5 y = 20 €
2.
Find
the
domain
of
each
of
the
following
functions.
Write
answers
in
interval
notation.
(5
points
each)
€
€
2x
1
(a)
f x =
+ x −3 x
()
x +8
(b)
m x = 2
x −2x − 8
()
3.
Give
the
domain
and
range
(in
interval
notation)
of
the
function
having
graph
below.
(8
points)
4.
Simplify
the
difference
quotient
(
) ( ) for
the
function
f
f x +h − f x
h
(x ) = 4x
2
+7x .
(8
points)
€
€
5.
The
point
2, −3 is
on
the
graph
of
y = f x .
What
is
the
corresponding
point
(where
does
this
point
move)
on
the
graph
of
y = −4 f 8x +2 .
(5
points)
(
)
()
( )
€
€
€
()
6.
The
graph
of
y = f x is
shown
below.
Sketch
the
indicated
graphs.
Be
sure
to
show
the
location
of
the
specific
points
marked
on
the
original
graph.
(7
points
each)
€
(a)
y = 2 f x − 4 + 1
€
(b)
y = − f 12 x −2
€
(
( )
)
2
7.
Put
the
quadratic
function
y = f x = 2x 2 +20x + 6 in
the
form
y = f x = a x − h + k by
completing
the
square.
(8
points)
€
€
8.
Find
an
equation
for
the
quadratic
function
having
graph
shown
below.
(7
points)
5
0
2.5
5
7.5
9.
A
projectile
is
launched
into
the
air,
and
its
height
above
the
ground
(in
feet)
after
x
seconds
is
given
by f x = −16x 2 + 112x + 42 .
What
is
the
maximum
height
reached
by
the
projectile,
and
when
is
this
height
achieved?
(8
points)
()
()
€
() (
)
10.
The
table
below
gives
values
for
two
functions,
f
and
g.
Find
the
indicated
values.
(4
points
each)
€
x
f(x)
x
g(x)
1
2
1
3
2
3
2
4
3
4
3
1
4
1
4
2
( ( ))
(a)
f g 2 ( ( ))
(b)
g f 1 €
1
x −5
11.
Suppose
f x = and
g x =
.
Find
a
simplified
formula
for
and
give
the
domain
of
the
2x
x
−8
function
f  g .
(10
points)
€
€
()
(
€
()
)