Stewart – Calculus 8e ET Chapter 1 Form A
1. If , find .
2. Solve each equation for x.
(a) (b)
3. Simplify the expression.
4. Fill in the blanks.
Let , where .
__________ __________
5. Determine whether f is even, odd, or neither.
6. Find the range of the function.
Stewart – Calculus 8e ET Chapter 1 Form A
7. The graphs of
and are given.
a) For what values of is ?
b) Find the values of and .
8. A spherical balloon with radius inches has volume
.
Find a function that represents the amount of air required to inflate the balloon from a radius of
inches to a radius of inches.
9. It makes sense that the larger the area of a region, the larger the number of species that inhabit the
region. Many ecologists have modeled the species-area relation with a power function and, in
particular, the number of species S of bats living in caves in central Mexico has been related to the
surface area A measured in of the caves by the equation
(a) The cave called mission impossible near puebla, mexico, has suface area of .
How many species of bats would expect to find in that cave?
(b) If you discover that species of bats live in cave estimate the area of the cave.
Stewart – Calculus 8e ET Chapter 1 Form A
10. The relationship between the Fahrenheit and Celsius temperature scales is given by the linear
function.
Complete the table and find the slope.
11. Plot the graph of the function in (a) the standard viewing window and (b) the indicated window.
f (x) = x, [-3, 3] [-5, 5]
12. Plot the graph of the function f in an appropriate viewing window.
f (x) = 2x – 5x + 4x + 27
13. Find the points of intersection of the graphs of the functions. Express your answers accurate to five
decimal places.
= 0.3 – 1.1x – 3.5; = –0.2 + 0.4x + 6.9
14. Determine whether f is one-to-one.
x
y
Stewart – Calculus 8e ET Chapter 1 Form A
15. If f (x) =
find f (–4), f (0), and f (1).
16. Refer to the graph of the function f in the following figure.
f(x)
12345678–1–2–3–4 x
1
2
3
4
5
–1
–2
–3
–4
–5
y
a. Find f (3).
b. Find the value of x for which (i) and (ii) .
c. Find the domain and range of f.
17. Let and . Find .
18. Find if
19. Let and . Find .
20. Find the function such that .
and
Stewart – Calculus 8e ET Chapter 1 Form A
Answer Key
Stewart – Calculus 8e ET Chapter 1 Form A
Stewart – Calculus 8e ET Chapter 1 Form A
Stewart – Calculus 8e ET Chapter 1 Form B
1. Find all solutions of the equation correct to two decimal places.
2. Solve each equation for x.
(a) (b)
3. Find the exact value of the expression.
4. Find the range of the function.
5. Express the function in the form of .
6. Plot the graph of the function f in an appropriate viewing window.
f (x) = 5x – 3x + 3x– x + 26
7. Find the points of intersection of the graphs of the functions. Express your answers accurate to five
decimal places.
= 0.3 – 1.2x – 3.4; = –0.2 + 0.2x + 6.3
Stewart – Calculus 8e ET Chapter 1 Form B
8. Determine whether f is one-to-one.
x
y
9. The graph of f is given. Sketch the graph of on the same set of axes.
y = f x( )
0.5 1 x
0.5
1
y
2
10. Find the inverse of f. Then sketch the graphs of f and on the same set of axes.
f(x) = ,
11. If f (x) =
find f (–1), f (0), and f (1).
Stewart – Calculus 8e ET Chapter 1 Form B
12. Refer to the graph of the function f in the following figure.
f(x)
12345678–1–2–3–4 x
1
2
3
4
5
–1
–2
–3
–4
–5
y
a. Find f (0).
b. Find the value of x for which (i) and (ii) .
c. Find the domain and range of f.
13. Determine whether the function is even, odd, or neither.
14. 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.
1–1 x
1
–1
y
Stewart – Calculus 8e ET Chapter 1 Form B
15. 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 13 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.
9
13
xx
xx
xx
xx
13 – 2x
x– 29
16. Use the vertical line test to determine whether the curve is the graph of a function of x.
12345–1–2–3–4–5 x
1
2
3
4
5
–1
–2
–3
–4
–5
y
17. Let and . Find .
18. Find if
19. Let and . Find .
Stewart – Calculus 8e ET Chapter 1 Form B
20. Find the function such that .
and
Stewart – Calculus 8e ET Chapter 1 Form B
Answer Key
Stewart – Calculus 8e ET Chapter 1 Form B
Stewart – Calculus 8e ET Chapter 1 Form C
Select the correct answer for each question.
____ 1. Find the points of intersection of the graphs of the functions. Express your answers accurate to five
decimal places.
f (x) = 0.5 – 1.8 + 2.2x – 4; = 2.8x – 4.3
a. (–0.55126, –5.84352),
(3.87001, 6.53604)
b. (–0.55126, –1.54352)
(0.28124, 10.83604)
(3.87001, 0.78748)
c. (–0.55126, –1.54352)
(3.87001, 0.78748)
d. (–0.55126, –5.84352),
(0.28124, –3.51252)
(3.87001, 6.53604)
____ 2. Starting with the graph of , find the equation of the graph that results from reflecting about
the line .
a.
b.
c.
d.
e.
____ 3. Use the Law of Exponents to rewrite and simplify the expression.
a.
b.
c.
d.
e.
Stewart – Calculus 8e ET Chapter 1 Form C
____ 4. Starting with the graph of , write the equation of the graph that results from shifting 5 units
right.
a.
b.
c.
d.
e.
____ 5. Suppose that the graph of is drawn on a coordinate grid where the unit of measurement
is an inch. How many miles to the right of the origin do we have to move before the height of the
curve reaches 2 ft? Rounded to the nearest mile.
a. 754.9 mi
b. 4,457,536.9 mi
c. 53,490,543 mi
d. 53,490,442.5 mi
e. 53,490,343 mi
____ 6. Find the exact value of the given expression.
tan–1
1
a.
b.
c.
d. 4
Stewart – Calculus 8e ET Chapter 1 Form C
____ 7. Use the laws of logarithms to expand the expression.
ln
a. ln [(x + 5)(x – 6)]
b. ln (x + 5) – ln (x – 6)
c. ln
d. ln
____ 8. Simplify the expression.
a. 9
b. 18
c. 216
d. 729
____ 9. Find a formula for the inverse of the function.
a.
b.
c.
d.
e.
Stewart – Calculus 8e ET Chapter 1 Form C
____ 10. Find the exact value of the expression.
a. 7
b. 8
c. 6
d. 4
e. 5
____ 11. The graphs of and are given. For what values of x is ?
a. 4, 2
b. 0
c.
d.
e. –4, 12
____ 12. Which of the following graphs is neither even nor odd?
a.
b.
c.
Stewart – Calculus 8e ET Chapter 1 Form C
____ 13. 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.
____ 14. What is the equation of this graph?
12345–1–2–3–4–5 x
1
2
3
4
5
–1
–2
–3
–4
–5
y
a.
b.
c.
d.
e.
Stewart – Calculus 8e ET Chapter 1 Form C
____ 15. Find the domain.
a.
b.
c.
d.
e.
____ 16. Find the range of the function.
a.
b.
c.
d.
e.
____ 17. The relationship between the Fahrenheit and Celsius temperature scales is given by the linear
function.
What is the F-intercept and what does it represent?
a. , Fahrenheit temperature corresponding to
b. , Celsius temperature corresponding to
c. 32, Celsius temperature corresponding to
d. 0, Fahrenheit temperature corresponding to
e. 32, Fahrenheit temperature corresponding to