In Exercises 13-18 graph each equation in a rectangular coordinate system . If two functions are given, graph both in same system. f ( x ) = x 3 − 4 x 2 − x + 4
In Exercises 13-18 graph each equation in a rectangular coordinate system . If two functions are given, graph both in same system. f ( x ) = x 3 − 4 x 2 − x + 4
Solution Summary: The author explains the function f(x)=x
In Exercises 13-18 graph each equation in a rectangular coordinate system. If two functions are given, graph both in same system.
f
(
x
)
=
x
3
−
4
x
2
−
x
+
4
System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.
10-2
Let A =
02-4
and b =
4
Denote the columns of A by a₁, a2, a3, and let W = Span {a1, a2, a̸3}.
-4 6
5
- 35
a. Is b in {a1, a2, a3}? How many vectors are in {a₁, a₂, a3}?
b. Is b in W? How many vectors are in W?
c. Show that a2 is in W. [Hint: Row operations are unnecessary.]
a. Is b in {a₁, a2, a3}? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your
choice.
○ A. No, b is not in {a₁, a2, 3} since it cannot be generated by a linear combination of a₁, a2, and a3.
B. No, b is not in (a1, a2, a3}
since b is not equal to a₁, a2, or a3.
C. Yes, b is in (a1, a2, a3} since b = a
(Type a whole number.)
D. Yes, b is in (a1, a2, 3} since, although b is not equal to a₁, a2, or a3, it can be expressed as a linear
combination of them. In particular, b =
+
+
☐ az.
(Simplify your answers.)
14
14
4. The graph shows the printing rate of Printer A. Printer B can
print at a rate of 25 pages per minute. How does the printing
rate for Printer B compare to the printing rate for Printer A?
The printing rate for Printer B is
than the rate
for Printer A because the rate of 25 pages per minute
is
than the rate of
for Printer A.
pages per minute
RIJOUT
40
fy
Printer Rat
Number of Pages
8N WA
10
30
20
Printer A
0
0
246
Time (min)
X
OR
16 f(x) =
Ef 16
χ
по
x²-2 410 | y = (x+2) + 4
Y-INT: y = 0
X-INT: X=0
VA: x=2
OA: y=x+2
0
X-INT: X=-2
X-INT: y = 2
VA
0
2
whole.
2-2
4
y - (x+2) = 27-270
+
xxx> 2
क्
above OA
(x+2) OA
x-2/x²+0x+0
2
x-2x
2x+O
2x-4
4
X<-1000 4/4/2<0 below Of
y
VA
X=2
X-2
OA
y=x+2
-2
2
(0,0)
2
χ
Precalculus: Mathematics for Calculus (Standalone Book)
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