# Determine the domain and range of the following functions

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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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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