Semester I Finals Study Guide - Answers
13)
1)
Domain: (− ∞,
−√6
)
2
2)
Quadrant 3
3)
(x − 2)(x + 2)(x2 + 4)
4)
⋃ ( √26 , ∞)
14)
25π
9 radians
15)
(x + 7)(x + 8)
2(x + 3)(x − 7)
16)
x=
17)
f −1 (8) = 2 ; Since it’s a one-to-one
3 log 2 (x) − log 2 (y) − 6
5)
3x - y = -13
6)
neither
7)
amplitude = 6
Period =​ 2π
3
(ln 8) + 2
5
8)
x=
9a)
f (g(x)) = 5x2 − 20x + 20
g (f (x)) = − 5x2 + 2
9b)
r = 1.97%
( gf )(x) =
5x2
2−x
3 ln 3 − ln 4
ln 3 − 2 ln 4
= − 1.14
function, we know every x-value has a
different y-value. This is not like a quadratic
function, where x-values can have the same
y-value. We now know that there is only one
possible value for f −1 (8) . Next, since the
function is an inverse (we can tell by the
symbol f −1 ), we know that all of the points
are switched. So, something like (2, 8) on a
regular function will have the point (8, 2) on
its inverse. This means that if f (2) = 8 is
true, then we can switch the numbers and
−1
state that f (8) = 2 is true.
18)
1−i
19)
y=
(f g)(x) = − 5x3 + 10x2
10a) x = -6
10b) x = 3, x = -3
11)
( 47 , −
12)
x=2
25
8 )
20)
4x + 2
x−1
x = 10
( 54 −2log 8 )
= 3.5 × 1026
21)
6 | 1 -2 5 1
6​ | ↓ 6 29 174
6​ |________________
1 4 29 175
All of the answers are positive, so 6 is
an upper limit of the function
22a) square root function
Natural logarithimic function
22b) reciprocoal
23) Domain: (− 4, 1 − √11] ⋃ [1 + √11, ∞)
34)
reflection over y-axis
shift 2 units left
shift 3 units up
35)
y = − e(x − 3) + 5
36)
[-7, 2)
37)
6.1°
38)
x = ln 4 = 1.4
39)
24)
y= -3cos (x) + 4
25)
c = 12
26)
y = x3 − 8x2 + 22x − 20x
27)
75 mL
28)
43.6 min.
29)
5.63 in. x 8,26 in.
30)
-2
31)
x=
32)
2√5
5
33)
(-4, 7)
2 ± 2i√5
3
± 1, ± 2, ± 5, ± 10, ± 31 , ± 32 , ± 55 ,
40)
sample answers:
x=0
x=
π
2
x=π