Practice Midterm 2
1. True/False
(a) If
x
y
10
then
yx )(log
.
(b)
15ln 2)2(ln
15
(c) The function
1)(
3
xxf
is an odd function.
(d) Let
x
xf 3)(
. If the graph of
)(xf
is reflected across the x-axis and
then shifted up four units, the new graph has the equation
43
x
y
.
(e) If
)(xf
is a periodic function of period
2
, then
)8()(
xfxf
provided x and
8x
are in the domain of
f
.
(f) An angle of
60
spans an arc length of
on a circle of radius 3.
(g) If
180
, then
)(cos
.
(h) The maximum and minimum values of the function
)(sin)(
f
are 1
and -1, respectively.
2. Complete the square to find the vertex of the parabola.
(a)
23 2 xxy
(b)
xxy 123
2
3. In each of the following, the graph on the right is a transformation of f, where f is
the graph on the left. Describe what transformations were applied to f and write a
formula in terms of f for the transformation.
(a)
)(xf
)( xg
-2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
(0,2)
(2,-2)
-2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
(2,-1/2)
(0,1/2)
(b)
)( xf
)(xh
