Calculus: Functions Question One
Calculus: Functions Question One
Calculus: Functions Question One
TUTORIAL 1
Functions
Question one
f ( x) 2 x 6
Let
Question two
In the following problems, an equation involving x and y is given. For each problem, determine
whether y is a function of x. If it is a one-to-one function, please specify and explain. If it is a
function, find the domain and range.
1. (x - 6) = 2(y 3)
2. x2 3y = 4
3. y3 4 = 0
4. |x| + |y| = 2
Question three
An office supply firm finds that the number of fax machines sold in year x is given
f ( x) 50 4 x
approximately by the function
1 2
x
2
Question four
Consider the set of all rectangles whose perimeter is 50 cm. For any one rectangle, once its width
W is measured, it is possible to do some computations that yield the area of the rectangle. Verify
this assertion by producing an explicit expression for area A as a function of width W. Find the
domain and range of your function.
Question five
Suppose that the brokerage firm in Example 6 (in textbook, please look up the relevant section)
decides to keep the commission charges unchanged for purchases up to and including $6000 but
to charge only 1.5% plus $15 for gold purchases exceeding $600. Express the brokerage
commission as a function of the amount x of gold purchased.
CALCULUS 2016
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CALCULUS 6
Question six
When you drive an Ace Rental compact car x kilometers in a day, the company charge f(x)
if
0 x 100
30
if
30 0.07( x 100)
f ( x)
dollars, where
x 100
Describe Ace Rentals pricing policy in plain English. (Be sure to interpret the constants 30,
0.07, and 100 that appear in the pricing formula)
Question seven
Heres a highly simplified version of the U.S federal income tax system. A taxpayer pays no
federal tax on the first $15,000 of annual income, 15% on the next $25,000 of income, and 28%
on all earnings above $40,000. Let x denote a taxpayers annual income (in dollars), and let T(x)
denote the tax owed (in dollars) at income level x.
The tax function T is piecewise-linear its graph consists of straight lines. Use this fact
to draw the graph of T(x) for 0 x 60,000.
Question eight
f ( x)
Let
1
x2
g ( x) x 2
and
f+g
iv.
f-g
ii.
f*g
iii.
f g
g f
v.
CALCULUS 2016
f/g
vi.
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