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Unformatted text preview: Math 16A
Kouba
Work sheet 2 1 .) Determine the constants a (and b) so that each of the following
funcﬁonsisconﬂnuousfora“vmuesofx. x2—7x+6
a) ﬁn = X6 , x 6
a , =6
aZXa x>1
b) fa): , —
2 , X<1
a+x
c) fa): a+1 , X<O
ax3+3 , x20
3 , X31
d) fa): ax2+b ,1<x32
5 , X>2
axb , xs—t
e) fa): 2x+3a+b p1<xs1
4 , X>1 2. An example of continuity as a measure of fairness—— A small city proposes the
following tax scheme for its residents in order to upgrade public parks. The annual
income and proposed amount of tax appear in the table below. :1. Sketch a graph of the amount of tax paid as a function of annual income x. b. In your opinion, is this tax scheme a fair one ? (Use the graph in part a.) Explain. Annual Income Tax $0 — $20,000 0.3% of income $20,001 — $40,000 the larger of $60 and 0.2% of income
$40,001 — $60,000 a flat fee of $20 plus 0.18% of income $60,001 and higher the larger of $128 and 0.16% of income .0 ho mo :0 Mo we 18 mo 40 HZOoZm
T805 qﬁ @V ...
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 Fall '08
 Kooba
 $20, $60, $0, $128

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