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Stewart_Calc_7ET ch01sec01
MULTIPLE CHOICE
1. The graphs of and are given. For what values of x is ?
a.
4, 2
b.
0
c.
d.
e.
–4, 12
2. Which of the following graphs is neither even nor odd?
a.
b.
c.
3. If the point is on the graph of an even function, what other point must also be on the
graph?
a.
b.
c.
d.
e.
None of these
4. If , evaluate the difference quotient .
a.
b.
c.
h
d.
e.
none of these
5. A box with an open top is to be constructed from a rectangular piece of card board with
dimensions in. by in. by cutting out equal squares of side at each corner and
then folding up the sides as in the figure.
Express the volume of the box as a function of .
a.
b.
c.
d.
e.
6. Find an expression for the function whose graph is the bottom half of the parabola
.
a.
b.
c.
d.
e.
7. A rectangle has perimeter m. Express the area of the rectangle as a function of the
length of one of its sides.
a.
b.
c.
d.
e.
8. If , find and simplify , where .
a.
b.
c.
d.
9. Find the domain of the function.
a.
(– ) ( )
b.
c.
d.
(– )
10. Find the domain and sketch the graph of the function. What is its range?
f (x) =
a.
D: (–, ); R: (–, 0] (3, )
c.
D: (–, ); R: (–, 3]
b.
D: (–, ); R: [0, )
d.
D: (–, ); R: [–1, )
11. Determine whether the function whose graph is given is even, odd, or neither.
1 2 3 4 5 6 7 8 9–1 x
1
2
3
4
–1
–2
–3
–4
–5
–6
y
1 2 3 4 5 6 7 8–1–2 x
1
2
3
4
5
6
7
8
9
–1
y
1 2 3 4 5 6 7 8 9 10 x
1
2
3
4
5
6
7
8
9
10
y
1 2 3 4 5 6 7 8–1–2 x
1
2
3
4
5
6
7
8
9
–1
y
a.
Even
b.
Neither
c.
Odd
12. Find the domain of the function
a.
b.
c.
d.
13. Sandy wishes to have a rectangular garden in her backyard. She has 40 ft of fencing with
which to enclose her garden. Letting x denote the width of the garden, find a function f in
the variable x that gives the area of the garden.
2 4 6 8 10–2–4–6–8–10 x
2
4
6
8
10
–2
–4
–6
–8
–10
y
x
y
a.
b.
c.
d.
14. The graph of the function is given. State the value of .
a.
b.
c.
d.
e.
15. The graph shown gives the weight of a certain person as a function of age. Find the age at
which the person started an exercise program.
a.
20
b.
54
c.
38
d.
e.
35
16. In the function , what must be the value d, if ?
a.
b.
c.
d.
e.
17. An open rectangular box with volume has a square base. Express the surface area of
the box as a function of the length of a side of the base.
a.
b.
c.
d.
e.
18. What is the equation of this graph?
a.
b.
c.
d.
e.
NUMERIC RESPONSE
1. The graphs of and are given.
Find the values of and .
2. Find the domain of the function.
1 2 3 4 5–1–2–3–4–5 x
1
2
3
4
5
–1
–2
–3
–4
–5
y
3. Determine whether f is even, odd, or neither.
4. Find the domain of the function.
5. Find the domain of the function.
6. Find the range of the function.
SHORT ANSWER
1. If f (x) =
find f (–4), f (0), and f (1).
2. Refer to the graph of the function f in the following figure.
a. Find f (1).
b. Find the value of x for which (i) and (ii) .
c. Find the domain and range of f.
3. Determine whether the function is even, odd, or neither.
f = (x)
1 2 3 4 5 6 7 8–1–2–3–4 x
1
2
3
4
5
–1
–2
–3
–4
–5
y
4. The following figure shows a portion of the graph of a function f defined on the interval
. Sketch the complete graph of f if it is known f is odd.
5. By cutting away identical squares from each corner of a rectangular piece of cardboard and
folding up the resulting flaps, an open box can be made. If the cardboard is 18 in. long and
9 in. wide and the square cutaways have dimensions of x in. by x in., find a function that
gives the volume of the resulting box.
1–1 x
1
–1
y
9
18
x x
x x
xx
x x
18 – 2x
x– 29
