Math B6A Lab 1
1. Determine the domain and range of the following functions:
a) f(x) = 2×2 ? 3x? 2
w ? 2
c) f(x) = ?
2 ? ? x
e) f(x) = 1
1 ? tan x
b) f(x) = ? x2 ? 2x? 3
d) f(x) = cos x
1 + sin x
2. Evaluate f(?3), f(0), and f(2) for the function defined by
f(x) =
{ x + 1 if x ??1 x2 if x > ?1
Then graph the function.
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Milad Vakili
Milad Vakili
3. Graph f(x) =
{ |x| if |x| ? 1 1 if |x| > 1
.
4. An open rectangular box with volume 2 m3 has a square base. Express the surface area of the box as a function of the length of a side of the base.
5. A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 10 in by 25 in by cutting out equal squares of of side x at each corner and then folding up the sides. Express the volume V of the box as a function of x.
6. Jason leaves Detroit at 2:00 PM and drives at a constant speed west along the I-94. He passes Ann Arbor, 40 miles from Detroit, at 2:50 PM. Express the distance traveled in terms of the time (in hours) elapsed.
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7. Evaluate the difference quotient for the given function. a) f(x) = 4 + 3x?x2
b) f(x) = 2
x + 1
8. Consider the functions f(x) = x2 + 10x + 30, g(x) = 3x + 5
x , and k(x) =
? x? 5.
a) Find each of the following and determine their domain.
i) (g ?k)(x) ii) (g ?k ?f)(x)
b) Evaluate (g ?k ?f)(1).
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9. Explain how each graph is obtained from the graph of y = f(x). a) y = f(x) + 2
b) y = f(x + 2)
c) y = f(x) ? 1
d) y = f(x? 4)
e) y = 3f(x)
f) y = f(3x)
g) y = ?f(x) ? 1
h) y = 8f
( 1
8 x
)
10. The graph of f is given below. Draw the graphs of the following:
a) y = f(x) ? 3
c) y = 1
2 f(x)
b) y = f(x + 1)
d) y = ?f(x)
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