Let x represent the number of country songs that Sierra puts on a playlist on her portable media player. Let y represent the number of rock songs that she puts on the playlist. For parts (a)-(e), write an inequality to represent the given statement. a. Sierra will put at least 6 country songs on the playlist. b. Sierra will put no more than 10 rock songs on the playlist. c. Sierra wants to limit the length of the playlist to at most 20 songs. d. The number of country songs cannot be negative. e. The number of rock songs cannot be negative. f. Graph the solution set to the system of inequalities from parts (a)-(e).
Let x represent the number of country songs that Sierra puts on a playlist on her portable media player. Let y represent the number of rock songs that she puts on the playlist. For parts (a)-(e), write an inequality to represent the given statement. a. Sierra will put at least 6 country songs on the playlist. b. Sierra will put no more than 10 rock songs on the playlist. c. Sierra wants to limit the length of the playlist to at most 20 songs. d. The number of country songs cannot be negative. e. The number of rock songs cannot be negative. f. Graph the solution set to the system of inequalities from parts (a)-(e).
Solution Summary: The author explains that the required inequality is xge 6, which represents the number of country songs Sierra puts on her portable media player.
Let
x
represent the number of country songs that Sierra puts on a playlist on her portable media player. Let
y
represent the number of rock songs that she puts on the playlist. For parts (a)-(e), write an inequality to represent the given statement.
a. Sierra will put at least
6
country songs on the playlist.
b. Sierra will put no more than
10
rock songs on the playlist.
c. Sierra wants to limit the length of the playlist to at most
20
songs.
d. The number of country songs cannot be negative.
e. The number of rock songs cannot be negative.
f. Graph the solution set to the system of inequalities from parts (a)-(e).
A graph of the function f is given below:
Study the graph of ƒ at the value given below. Select each of the following that applies for the value a = 1
Of is defined at a.
If is not defined at x = a.
Of is continuous at x = a.
If is discontinuous at x = a.
Of is smooth at x = a.
Of is not smooth at = a.
If has a horizontal tangent line at = a.
f has a vertical tangent line at x = a.
Of has a oblique/slanted tangent line at x = a.
If has no tangent line at x = a.
f(a + h) - f(a)
lim
is finite.
h→0
h
f(a + h) - f(a)
lim
h->0+
and lim
h
h->0-
f(a + h) - f(a)
h
are infinite.
lim
does not exist.
h→0
f(a+h) - f(a)
h
f'(a) is defined.
f'(a) is undefined.
If is differentiable at x = a.
If is not differentiable at x = a.
The graph below is the function f(z)
4
3
-2
-1
-1
1
2
3
-3
Consider the function f whose graph is given above.
(A) Find the following. If a function value is undefined, enter "undefined". If a limit does not exist, enter
"DNE". If a limit can be represented by -∞o or ∞o, then do so.
lim f(z)
+3
lim f(z)
1-1
lim f(z)
f(1)
= 2
=
-4
= undefined
lim f(z) 1
2-1
lim f(z):
2-1+
lim f(x)
2+1
-00
= -2
= DNE
f(-1) = -2
lim f(z) = -2
1-4
lim f(z)
2-4°
00
f'(0)
f'(2)
=
=
(B) List the value(s) of x for which f(x) is discontinuous. Then list the value(s) of x for which f(x) is left-
continuous or right-continuous. Enter your answer as a comma-separated list, if needed (eg. -2, 3, 5). If
there are none, enter "none".
Discontinuous at z =
Left-continuous at x =
Invalid use of a comma.syntax incomplete.
Right-continuous at z =
Invalid use of a comma.syntax incomplete.
(C) List the value(s) of x for which f(x) is non-differentiable. Enter your answer as a comma-separated list,
if needed (eg. -2, 3, 5).…
A graph of the function f is given below:
Study the graph of f at the value given below. Select each of the following that applies for the value
a = -4.
f is defined at = a.
f is not defined at 2 = a.
If is continuous at x = a.
Of is discontinuous at x = a.
Of is smooth at x = a.
f is not smooth at x = a.
If has a horizontal tangent line at x = a.
f has a vertical tangent line at x = a.
Of has a oblique/slanted tangent line at x = a.
Of has no tangent line at x = a.
f(a + h) − f(a)
h
lim
is finite.
h→0
f(a + h) - f(a)
lim
is infinite.
h→0
h
f(a + h) - f(a)
lim
does not exist.
h→0
h
f'(a) is defined.
f'(a) is undefined.
If is differentiable at x = a.
If is not differentiable at x = a.
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