assignment 3, Jan 16, section 2.1
Cu
ent Score : – / 82 Due : Thursday, Fe
uary XXXXXXXXXX:00 PM CST
1. –/5 points TanApCalcBr XXXXXXXXXX.
Let f be the function defined by the equation below.
f(x) = 4x - 3
Find the following.
f(3) =
f(2) =
f(0) =
f(a) =
f(a + 1) =
2. –/13 points TanApCalcBr XXXXXXXXXXMI.SA.
This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points fo
the skipped part, and you will not be able to come back to the skipped part.
Tutorial Exercise
Let g be the function defined by Find and
3. –/3 points TanApCalcBr XXXXXXXXXX.
Let f be the function defined by the equation below.
Find the following.
f(0) =
f(1) =
f(11) =
assignment 3, Jan 16, section 2.1 (Homework)
Jeremy Alameda
(spring 2013) Math 146 Applied Calculus I at noon, section 146-03, Spring 2013
Instructor: Stuart Farm
WebAssign
g(x) = −x2 + 3x. g(a + h), g(−a), g( ),a a + g(a), .1
g(a)
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4. –/5 points TanApCalcBr XXXXXXXXXX.
Refer to the graph of the function f in the following figure.
(a) Find f(0).
f(0) =
(b) Find the value of x for which f(x) = 3 and f(x) = 0.
(i) f(x) = 3
x =
(ii) f(x) = 0
x =
(c) Find the domain of f.
(d) Find the range of f.
(0, 6)
(−2, 6)
[−2, 6]
[0, 6]
[−2, 6]
(−2, 6)
[0, 6]
(0, 6)
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5. –/7 points TanApCalcBr XXXXXXXXXX.
Refer to the graph of the function f in the following figure.
(a) Find
=
(b) Find the values of x co
esponding to the point(s) on the graph of f located at a height of 5 units above the x-axis.
x = (smaller value)
x = (larger value)
(c) Find the point on the x-axis at which the graph of f crosses it.
x =
What is f(x) at this point?
f(x) =
(d) Find the domain and range of f. Domain:
Range:
6. –/1 points TanApCalcBr XXXXXXXXXX.
Find the value of c such that the point P(a, b) lies on the graph of the function f.
c =
f(7).
f(7)
[−2, 6]
(−1, 9)
(−2, 6)
[−1, 9]
(−2, 6)
(−1, 9)
[−1, 9]
[−2, 6]
f(x) = x + c; P(3, 6)16 − x2
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7. –/1 points TanApCalcBr XXXXXXXXXX.
Find the domain of the function.
8. –/1 points TanApCalcBr XXXXXXXXXX.
Find the domain of the function.
9. –/1 points TanApCalcBr XXXXXXXXXX.
Find the domain of the function.
(− , )
(3, )
[3, )
(− , 3]
(− , 3)
f(x) = 9x + 4
x − 7
(− , 7) (7, )
(− , )
(− , −4) (4, )
− , − , 4
9
4
9
(− , −9) (9, )
[3, )
(− , )
(− , 3)
(− , 3]
(3, )
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10.–/1 points TanApCalcBr XXXXXXXXXX.
Find the domain of the function.
h(x) =
x(x − 8)
x − 5
[5, )
[5, 8) (8, )
(− , )
(− , 0) (0, 8) (8, )
(8, )
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11.–/10 points TanApCalcBr XXXXXXXXXX.
Let f be a function defined by the rule
(a) Find the domain of f.
(− , 7)
(− , )
(−7, )
(− , −7)
(−7, 7)
(b) Compute f(x) for
=
=
=
=
=
=
=
=
(c) Use the results obtained in parts (a) and (b) to sketch the graph of f.
f(x) = x2 − x − 7.
x = −3, −2, −1, 0, , 1, 2, 3.1
2
f(−3)
f(−2)
f(−1)
f(0)
f(1/2)
f(1)
f(2)
f(3)
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12.–/3 points TanApCalcBr XXXXXXXXXX.
Sketch the graph of the function with the given rule.
Find the domain of the function.
(− , )
(− , −2)
[−2, 2]
(− , 2]
(−2, )
Find the range of the function.
(− , 4)
(− , −4]
[−4, )
[4, )
(− , 4]
f(x) = 4 − x2
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13.–/3 points TanApCalcBr XXXXXXXXXX.
Find the domain and sketch the graph of the function.
Domain:
What is its range?
14.–/3 points TanApCalcBr XXXXXXXXXX.
Sketch the graph of the function with the given rule.
g(x) = x − 2
(− , −2) (2, )
(− , )
[0, )
(− , 0) (0, )
[2, )
(− , −2) (2, )
(− , )
[2, )
[0, )
(− , 0) (0, )
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Find the domain of the function.
[4, )
(− , −4]
[−4, 4]
(−4, 4)
(− , )
f(x) =
−x − 4 if x < −4
0 if −4 ≤ x ≤ 4
x + 4 if x > 4
Find the range of the function.
(− , −8]
(0, )
[8, )
[0, )
(− , 0]
15.–/2 points TanApCalcBr XXXXXXXXXX.
The volume of a sphere of radius r is given by
V(r) = (4/3)pi r^3 .
Compute V(3.1) and V(3). (Round your answers to the nearest whole number.)
V(3.1) =
V(3) =
16.–/1 points TanApCalcBr XXXXXXXXXX.
The surface area S of a single-celled organism may be found by multiplying 4π times the square of the radius r of the cell. Express S as a
function of r.
S(r) =
17.–/2 points TanApCalcBr XXXXXXXXXX.
Social Security recipients receive an automatic cost-of-living adjustment (COLA) once each year. Their monthly benefit is increased by the
amount that consumer prices increased during the preceding year. Suppose that consumer prices have increased by 6.2% during the
preceding year.
(a) Express the adjusted monthly benefit of a Social Security recipient as a function of his or her cu
ent monthly benefit.
I(x) =
(b) If Ha
ington's monthly Social Security benefit is now $540, what will be his adjusted monthly benefit?
$
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18.–/2 points TanApCalcBr XXXXXXXXXX.
An efficiency study conducted for Elektra Electronics showed that the number of Space Commander walkie-talkies assembled by the
average worker t hr after starting work at 8 A.M. is given by
N(t) = -t^3 + 6t^2 + 15t text( for ) \(0<=t<=4\)
How many walkie-talkies can an average worker be expected to assemble between 8 and 9 A.M.? Between 9 and 10 A.M.?
8 - 9 A.M. walkie-talkies
9 - 10 A.M. walkie-talkies
19.–/1 points TanApCalcBr XXXXXXXXXX.
Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.
If f(a) = f(b), then a = b.
True, because a function is a rule that assigns to each element in a set A one and only one element in a set B.
True, because a function is a rule that assigns one and only one element in a set A to each element in a set B.
True, because a function is a rule that assigns to each element in a set A a number of elements in a set B.
False. Take Then but
False. Take Then but
20.–/1 points TanApCalcBr XXXXXXXXXX.
Find the slope of the line that passes through the pair of points. (If an answer is undefined, enter UNDEFINED.)
21.–/1 points TanApCalcBr XXXXXXXXXX.
Determine whether the lines AB and CD are parallel.
parallel
not parallel
f(x) = x, a = 1, b = −1. f(1) = 1 = f(−1), a ≠ b.
f(x) = x2, a = 1, b = −1. f(1) = 1 = f(−1), a ≠ b.
(−a + 2, b − 3) and (a + 2, −b)
A(2, 1), B(2, 5) and C(−2, −5), D(−2, −1)
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22.–/1 points TanApCalcBr XXXXXXXXXX.
Determine whether the lines AB and CD are perpendicular.
perpendicula
not perpendicula
23.–/1 points TanApCalcBr XXXXXXXXXX.
Find an equation of the line that passes through the point and has the indicated slope m. (Let x be the independent variable and y be the
dependent variable.)
24.–/1 points TanApCalcBr XXXXXXXXXX.
Find the distance between the given points.
25.–/1 points TanApCalcBr XXXXXXXXXX.
Find an equation of the circle that satisfies the given conditions.
Radius 7 and cente
A(4, 0), B(3, −5) and C(5, 5), D(−10, 3)
(1, 2); m = − 1
2
(−1, 3) and (3, 14)
(−7, −6)
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26.–/2 points TanApCalcBr XXXXXXXXXX.
Refer to the figure below. Suppose a fleet of 100 automobiles is to be shipped from an assembly plant in town A to town D. They may be
shipped either by freight train along