Corrections for Advanced Functions
Question
Correct Answer
Getting
4d
D = {x e= R},
R={ye=Ri-3<y<3}
(Correct in solutions manual)
Started
1.2
4d
Entire number line should be shaded on graph.
Mid-Chapter
2b
D = [0, 10
2c
R= [10, 50
I
]
'l
Location
Mid-Chapter
l
Review
l
Review
3
(-4,-10)
7c
g(x) = -2(23(X l)) + 4
1.4
9c
(-1,23)
1.4
12
Graph of h(x) (green) should be reflection of graph ofj'(x) over x-
l
1.4
1.4
l
6
{1 s + 0.02(X - soo), if x > soo
1.6
12
Chapter
3
discontinuous at p = l 5; continuous at O < p < 15
R = {f(X) € R lf(X) > -1 }
1.6
15,d O < x < 500
I
Review
/
I
Labels should be in degrees, not radians. Curves should not have
arrowheads at ends.
l
6b
I
axis.
1.5
l
17a
{24 + 0.03x, if x > 200
7a
(-2, 17)
9a
$11500
9b
{0.12X-ssoo, ifx>soooo
Location
Question
Correct Answer
Mid-Chapter
lb
750a Oa 250a l lO0a 400 m3/month
3b
t = 2; Answers may vary. For example: The graph has a vertex at
(2, 21 ). It appears that a tangent line at this point would be
Chapter
Review
30,7x<200
(Correct in solutions manual)
Chapter SelfTest
Chapter SelfTest
Chapter SelfTest
0.05, if x < 50000
Review
Mid-Chapter
Review
horizontal. (f(2'l) f'99))
0.02
2.5
2
Chapter
4a
Review
0 mm Hg/s
Answers may vary. For example, because the unit of the equation
is years, you would not choose 3 < t < 4 and 4 < t < 5. A better
choice would be 3.75 < t < 4.0 and 4 < t < 4.25.
I
Chapter
Review
8
art
Question
Correct Answer
8
The values of x that make flx) = 0 = n (Located on arrovv above
l
Location
Getting
l
box with The zeros are -2 and -6.)
Started
y = x2 ; reflection in the x-axis, vertical stretch by a factor of 4.8,
3.4
6f
and horizontal translation 3 units right
(Correct in solutions manual)
(-11, -3), (-4, -2), (10, 6)
3.5
3c
x-6
3.5
6d
.
x2
+2X - 8 remainder
-4
l
l
8a
2
Graph is incorrect; should be graph of y = (X + 6)(X + 5)(X - 2)
AS X -=> - co, y -=> + oo, and as X-> 00, y -+ - oO.
Location
Question
Correct Answer
4.1
2d
Review
"
l
3.6
Chapter
l
l
]
5
4.1
14c
0.45 s, 3.33 s (Correct in solutions manual)
4.1
16
x = -3, x = -2, x = 5 (Correct in solutions manual)
4.2
17b
Move the terrns with variables to one side and constants to the
1
I
2
0, - , -3 (Correct in solutions manual)
l
:
l
2e
3.4
other. Graph y = 2" - x and y = 4 on a graphing calculator and
determine where y = 2" - x is below y = 4.
-3.93 < x < 2.76
4.2
lla
4.2
19b
4.2
19d
{xaeRi-3>y>3}
{X€RIX<-3};(-"))-3)
graph should be shaded from -3 to left
Mid-Chapter
6a
Answers may vary. For example, 3x + 1 > x + 15
6b
Answers may vary. For example, 5x-1 < x - 33
6c
Answers may vary. For example, x - 3 < 3X-l < x-13
l
2
Review
Mid-Chapter
Review
Mid-Chapter
Review
3
4.3
6e
4.3
18
x-1 < or x > 2 (Correct in solutions manual)
4.4
2e
O<x<2
4.4
4a
4.4
4b
4.4
lla
7 (Correct in solutions manual)
Answers may vary. For example, (4.5, 3).
(Correct in solutions manual)
Remove graph.
4.4
llb,llc
Answers should be combined.
Chapter
3b
(Correct in solutions manual)
-3.10 (Correct in solutions manual)
6a
Answers may vary. For example, 3X + 1 > x + 17
-'H< x or x > 3 (Correct in solutions manual)
Review
Chapter
Review
I
Answers may vary. For example, -x + 1 < 3
Chapter
6b
Answers may vary. For example, 4x - 4 > x-16
6c
Answers may vary. For example, 3X + 3 < x - 21
6d
Answers may vary. For example, x -19 < 3x-1 <x -3
Review
Chapter
Chapter
I
Review
l
Review
7b
Chapter Self-
23
x e (-oo, -8 ]
Review
8a
l
Chapter
1
{xe=IRi-2<X<7}
I
Test
]
Question
Getting
2f
a-b
3c
l
2a-3b'a" 3
Started
Getting
Correct Answer
l
Location
-ax + s, x f- -2, 3
Getting
I
Started
4d
Getting
4f
Started
Getting
3X+6
,r, x # 0, 3
Started
-2a + 50
(a+3)(a-5)(a-4)'x# '4'5
5d
X=ll
9a
D = {x e R}
R={yeR}
y-intercept = 8
x-intercept = -4
negative on (-oo, -4)
positive on (-4, -oo)
increasing on (-oo,oo)
Started
5.1
1
equation of reciprocal: y = 2x+8
5.1
9b
D = {x e R}
R={yeR}
y-intercept = -3
3
x-intercept = - 4
3
positive on (-oo, - - )
4
3
negative on (- - , oo)
4
decreasing on (-00, 00)
1
equation of reciprocal: y = -4x-3
5.1
9c
D = {x e R}
R={yeRiy< -12.25}
y-intercept = 12
x-intercepts = , -3
decreasing on (-C0, 0.5)
l
l
increasing on (0.5, oo)
positive on (-oo,-3)
negative on (-3, 4)
..
1
x2-x-12
equation of reciprocal: y =
5.1
9d
D = {x e R}
R={yeRiy<0.5}
y-intercept = -12
x-intercepts = 3, 2
increasing on (-oo, 2.5)
decreasing on (2.5, oo)
negative on (-oo, 2) and (3, oo)
positive on (2, 3)
l
equation of reciprocal: y-2X
= 2 +10X-12
5.1
12e
D= {X e Ri 1 <x< 10000},
R={yeRil<y<10000}
1
5.2
ld
D; The function in the denominator has zeros at x = l and x = -3.
l
the rational function has vertical asymptotes as x = l and x = -3.
5.2
2i
1
vertical asymptote at x = - 2; horizontal asymptote at
J=2
5.2
3c
x+2
I
y=
5.3
2e
D={xeRix;=-2}
R={yeRiy=-O}
5.3
3f
,3
positive: (-oo, -1) and (2, oo)
3
negative: (-1, 'g)
5.3
4a
5.3
4b
5.3
4c
5.3
4d
5.3
5c
x = -3 ; As x -> -3 from the left, y -> -oo. As x -> -3 from the
right, y -> oo,
x = 5; As x -> 5 from the left, y -> -oo. As x -> 5 from the right, y
-) CO,
11
1
x = H; As x -> 3 from the left, y -> -00. As x-> 3 from the right, y
+.
11
1
x = -,;; As x -> -;z from the left, y -> -a:i. As x -> -';, from the
right, y -> 00,
vertical asymptote at x = 11
4
1
1
horizontal asymptote at y = z
D={xeRix;=-2}
R= {y e Ri y-7,}
x-intercept = -5
y-intercept = -5
l
l
j(x) is positive on (-ar, -5) and (2, oo) and negative on (-5, 2).
11
The function is decreasing on (-oo, '5) and on ('g, oo). The function
5.3
7a
is never increasing.
The equation has a general vertical asymptote at
1
8
x = -'-. The function has a general horizontal asymptote at y = - .
n
n
111
The vertical asymptotes are - - , - - , - - , and -1 . The horizontal
842
asymptotes are 8, 4, 2, and 1 , The function contracts as n increases.
l
The function is positive on (-oo, -;) and (0, oo). The function is
1
negative on (- n, O).
5.3
7c
8
The horizontal asymptote is y = ;;, but because n is negative, the
1
value of y is negative. The vertical asymptote is x = -';, but
because n is negative, the value of x is positive. The function is
negative on
1
(-oo, 0) and (-';;, oo). The function is positive on
1
(0,-.-).
5.3
8
j(x) will have a vertical asymptote at x = l ; g(x) will have a
l
horizontal asymptote at x = '>. j(x) will have a horizontal asymptote
at x = 3 ; g(x) will have a vertical asymptote at x = E.
1
5.3
10
The concentration increases over the 24 h period and approaches
approximately 1.85 mg/L.
5.3
14a
j'(x:) and m(x) - -
5.3
14b
Mid-Chapter
2a
g(x)
D = {x e R} ; R = {y e R} ; y-intercept = 6;
Review
3
3
2
2
x-intercept = - - ; negative on (-oo, - - ); positive on
3
(- - ,oo); increasing on (-oo,oo)
2
Mid-Chapter
2b
Review
Mid-Chapter
2c
Review
Mid-Chapter
2d
D = {x e R} ; R = {y e Ri y > -4}; y-intercept = -4; x-intercepts
are 2 and -2; decreasing on (-oo, 0); increasing on (0, co); positive
on (-oo,-2); increasing on (2, oo);negative on (-2, 2)
D = {x e R} ; R = {y e Ri y > 6}; y-intercept = 6; no x-intercepts;
function will never be negative; decreasing on (-oo, 0); increasing
on (0, oo)
D = {x e= R}; R= {y e R}; y-intercept=-4;
x-intercept = -2; function is always decreasing; positive on (oo, 2); negative on (-2, oo)
Review
Mid-Chapter
4a
x = 2;-horizontal asymptote
4e
x = -5 and x = 3 (delete "vertical asymptotes")
Review
Mid-Chapter
Review
5
x-2
)'=
Review
Mid-Chapter
6a
Review
x
7
l
-))'=1;.)'=--;.)'= , 5.)'=0
4x+2X-15
I
Mid-Chapter
1
1
1
D = {x e R i x # 6} ; vertical asymptote: x = 6; horizontal
asymptote: y = 0; no x-intercept;
5
y-intercept: - - ; negative when the denominator is negative;
6
Mid-Chapter
6b
Review
Mid-Chapter
6c
Mid-Chapter
I
Review
positive when the numerator is positive;
x - 6 is negative on x < 6; flx) is negative on (-oo, 6) and positive
on (6, oo); function is decreasing on
(-oo, 6) and (6, oo)
D = {x e R i x * -4} ; vertical asymptote: x = -4; horizontal
asymptote: y = 3 ; x-intercept: x = 0;
y-intercept: §O) = 0; function is increasing on (-(X), -4) and (-4, oo);
positive on (-CO, -4) and (0, oo); negative on (-4, 0)
D = {x e Ri x * 2}; straight, horizontal line with a hole at x = -2;
always positive and never increases or decreases
6d
1
1
D = {X e= R i x * H} ; vertical asymptote: x = >; horizontal
Review
1
asymptote: y = H; x-intercept: x = 2;
11
y-intercept: §0) = 5; function is increasing on (-CX), E) and (>, 00)
5.4
1
Yes; answers may vary, For example, substituting each value for x
in the equation produces the same value on each side of the
5.4
6d
x=0andx=l
5.4
6e
13
5.4
7e
x = -1 .72, 2.72
5.4
8a
equation, so both are solutions.
x=-landx= - 27
x+l x+3
x-2x-4
Multiply both sides by the LCD, (X - 2) (X -4).
X+l
(X-2)(X-4) x-2
x+3
=(X-2)(X-4) x-4
(X-4)(X+ 1)=(X-2)(X+3)
..2
2
Simplify
the equation
so that
0 is on one side of the equation.
Simplify.x
-3X-4=x
+x-6
22
x -x -3x-x-4+6
=x22
-x +x-x-6+6
-4x+2=O
-4x=-2
1
X= -
2
After 6666.67 min
5.4
13b
l.05min
5.5
la
(-oo, l) and (3, oo)
I
5.5
4a
-5 < x < -4.5
5.5
4f
l
12a
l
1
5.4
l
7
-l <x< -andx>4
8
5d
t<-5and O<t<3
6a
5.5
6b
5.5
6c
x e (-6, -13 orx e (4, oo)
x e (-oo, -3)
x e (-4, -2] orx e (-1, 2]
5.5
7a
5.5
8c
It would be difficult to find a situation that could be represented by
these rational expressions because very few positive values of t
yield a positive value of y.
5.5
9
Yes, as §t) - g(t) > O on the interval (0, 0.31 ). For instance, the
l
5.5
5.5
l
l
l
l
1
x< -6 -1<X< 2,X>2
bacteria in the tap water will outnumber the bacteria in the pond
water after t = 0.2 days.
5.5
l0a
] < o
5.5
11
whenl<x<5
5.5
14
}4.48o < x < 165.52o and 180o < x < 360o
5.5
15
Oo<x<2o
5.6
5d
11.72
5.6
6a
slope = 286. 1 ; vertical asymptote: x = -0.3
5.6
6b
slope = 2.74; vertical asymptote: x = -5
5.6
6c
3
2x
.
5
slope = A4.64; verhcal
asymptote:
x=--
5.6
7b
o
5.6
9b
5.6
l0a
5.6
lOb
-$ 1 .22 per T-shirt
-11 houses per month
-1 house per month
5.6
12d
The instantaneous speed for a specific time, t, is the acceleration of
Chapter
lb
Review
Chapter
lc
the ot,ject at this time.
D= {xe R};R= {ye Riy> -10.125};
x-intercept = 0.5 and -4;
positive on (-oo, -4) and (0.5, co);
negative on (-4, 0.5);
decreasing on (-oo, -1.75); increasing on (-1 .75, oo)
D = {xe R} ; R = {y e Ri y > 2}; no x-intercepts;
y-intercept = 2; decreasing on (-co, 0); increasing on (0, oo); always
Review
positive; never negative
Chapter
Review
4
The locust population increased during the first
1.4 years, to reach a maximum of 1 287 000. The population