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(MATH005)quiz3_math005_by_PPSpider.pdf
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Tutorial: Duration: Math 005 quiz03 Name: ID Number:
1. Solve for x: ex . e.x 2 = 3 4

3
u .
Hint. First solve
x
by the quadratic equation, then solve e= u. The .nal answer is that x
u
=
24
is the ln of a number.
(a) x = ln(2) (b) x = ln(3) (c) x = ln(4) (d) x = ln(5) (e) x = ln(6)
2. From sales record, thereisa linear relationship0.6p+0.03q = 12.6between theweekly demand(q kg) and price(pdollarperkg)ofthechickenwings soldinBBQSupermarket.Atwhat weekly sales level can BBQ Supermarket obtain maximumweekly revenue?
(a) 260 kg (b) 270 kg (c) 290 kg (d) 210 kg (e) 230 kg
3. Given the graph of the function f(x)= x(x . 1)(x . 2) in the .gure on the left below, which curve (sketched with di.erent widths) in the .gure on the right is the graph of g(x)= .2x(x . 1)(x . 2). 1
(a) A (b) B (c) C (d) D (e) E
4. Solve x2 . x . 2 0:
(a) x .1 or2 x (b) x .1 or2 x (c) .1 x 2
(d) x .1 and2 x (e) x .1 or2 x
x.2
5. Find the domain and intercepts for the rational function f(x)=
x+3
(a)
Domain: x = .3, x-intercept=2 and y-intercept= .

(b)
Domain: x ..3, x-intercept=2 and y-intercept=

=

(c)
Domain:


2
3
2
3
x ..3, x-intercept=2 and y-intercept= .
=
2
3
(d) Domain: x ..3, x-intercept=-2 and y-intercept= .
=
2
3
(e) Domain: x ..3, x-intercept=3 and y-intercept= .
=
2
3
6. Determine whichone of the quadratic functions f(x)below has the propertythat it attains its maximum at the coordinate(.2, 1/2):
(a)
f(x)= .(2x +1)2 +

(b)
f(x)=(


1
2
1 2
x +1)2 +
1 2
(c) f(x)= .(
1 2
x +1)2 +
1
21
2
(d)
f(x)= +(2x +1)2 +

(e)
f(x)= .(


1 2
x +1)2 .
1 2
7. Supposetheunemploymentratehasbeenrisingata constantrateof0.5 thousandpermonthforthelast few years. It is anticipated that the trend will continue for another year. Suppose the unemployment .gure is 22 thousand at thebeginning of thisyear. What willbe the unemployment at the end of this year?
(a) 34,000 (b) 30,000 (c) 12,000 (d) 28,000 (e) 6,000
8. Determine the vertical axis of symmetry of the graph of the function y = f(x)= .x2 . 8x +12.
(a) x =4 (b)
x
=
3 2
(c) x = .4 (d)
x
=
5 2
(e)
x
=
7 2
9. Thepopulation (in millions) of the state of Michigan USA, is7.81.0058t where t is thenumberofyears fromthe startof 1960.In what monthandyeardidMichiganachieveapopulationof8.3 million?
(a) July 1972 (b) April 1975 (c) February 1978 (d) September 1970 (e) April 1985
f(2+h). f(2)
10. Let f(x)=2x . x2 +1. Simplify .
h
(a) .h. 2 (b) .h. 1 (c) .h (d) .h+1 (e) .h+2
(2x . 1)
11. Find the domain of the function f(x)= .
(x +3)(x . 1)
(a)
All real numbers

(b)
All realnumbers except1/2

(c)
All realnumbers except1/2, .3, and1

(d)
All real numbers except .3and1

(e)
All real numbers < 1/2


12. A Hong Kong bank lists the following rates for buying and selling currency into Hong Kong dollars:
Buy Sell
US Dollar 7.75