The rational functions studied in this section all have the characteristic that the numerator and denominator do not share a common variable factor. We now investigate rational functions for which this is not the case. For Exercises 111–114, a. Write the domain of f in interval notation. b . Simplify the rational expression defining the function. c. Identify any vertical asymptotes. d . Identify any other values of x (other than those corresponding to vertical asymptotes) for which the function is discontinuous. e . Identify the graph of the function. f ( x ) = 2 x + 10 x 2 + 9 x + 20
The rational functions studied in this section all have the characteristic that the numerator and denominator do not share a common variable factor. We now investigate rational functions for which this is not the case. For Exercises 111–114, a. Write the domain of f in interval notation. b . Simplify the rational expression defining the function. c. Identify any vertical asymptotes. d . Identify any other values of x (other than those corresponding to vertical asymptotes) for which the function is discontinuous. e . Identify the graph of the function. f ( x ) = 2 x + 10 x 2 + 9 x + 20
Solution Summary: The author explains the domain of the function f(x)=2x+10x
The rational functions studied in this section all have the characteristic that the numerator and denominator do not share a common variable factor. We now investigate rational functions for which this is not the case. For Exercises 111–114,
a. Write the domain of f in interval notation.
b. Simplify the rational expression defining the function.
c. Identify any vertical asymptotes.
d. Identify any other values of x (other than those corresponding to vertical asymptotes) for which the function is discontinuous.
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Things Quadratics! Part 1 X
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The table below shows the acreage, number of visitors, and total revenue of state parks and recreational areas in Massachusetts, New York, and Vermont in 2010.
State Acreage (in thousands) Visitors (in thousands) Revenue (in thousands)
Massachusetts 350 35,271 $12,644
New York 1,354 56,322 $85,558
Vermont 69 758 $10,969
Select the three true statements based on the data in the table.
A.
Vermont had the highest revenue per acre of state parks and recreational areas.
B.
Vermont had approximately 11 visitors per acre of state parks and recreational areas.
C.
New York had the highest number of visitors per acre of state parks and recreational areas.
D.
Massachusetts had approximately 36 visitors per acre of state parks and recreational areas.
E.
New York had revenue of approximately $63.19 per acre of state parks and recreational areas.
F.
Massachusetts had revenue of approximately $0.03 per acre of state parks and recreational areas.
a) show that the empty set and sigletonset
are convex set.
6) show that every sub space of linear space X
is convex but the convers heed not be true.
c) let Mand N be two convex set of
a linear Space X and KEF
Show that MUN is conevex and
(ii)
M-N is convex or hot
A
and is MSN or NSM show that
MUN convex or not,
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