Stewart – Calculus 8e ET Chapter 1 Form C
____ 18. If and , find a function g such that .
a.
b.
c.
d.
e.
Stewart – Calculus 8e ET Chapter 1 Form C
____ 19. The graph of the function follows. Choose the graph of
369–3–6–9 x
3
6
9
–3
–6
–9
y
a.
369–3–6–9 x
3
6
9
–3
–6
–9
y
c.
369–3–6–9 x
3
6
9
–3
–6
–9
y
b.
369–3–6–9 x
3
6
9
–3
–6
–9
y
d.
369–3–6–9 x
3
6
9
–3
–6
–9
y
Stewart – Calculus 8e ET Chapter 1 Form C
____ 20. Which of the following graphs is the graph of the function?
Graph 1
12–1–2
Graph 2
1234–1–2–3–4
Graph 3
1234–1–2–3–4
a. Graph 2
b. Graph 1
c. Graph 3
Stewart – Calculus 8e ET Chapter 1 Form C
Answer Key
Stewart – Calculus 8e ET Chapter 1 Form D
Select the correct answer for each question.
____ 1. Find all solutions of the equation correct to two decimal places.
a.
b. ,
c. , ,
d. ,
e. ,
____ 2. Use the Law of Exponents to rewrite and simplify the expression.
a.
b.
c.
d.
e.
Stewart – Calculus 8e ET Chapter 1 Form D
____ 3. Starting with the graph of , write the equation of the graph that results from shifting 3 units
right.
a.
b.
c.
d.
e.
____ 4. Find the inverse function of .
a.
b.
c.
d.
e.
____ 5. Find (a) for the function f and the real number a.
;
a. 2
b. 1
c. 3
d. 0
Stewart – Calculus 8e ET Chapter 1 Form D
____ 6. Find the inverse of f. Then sketch the graphs of f and on the same set of axes.
,
a. ,
f = f –1
12345 x
1
2
3
4
5
y
c. ,
f = f –1
12345 x
1
–1
–2
–3
–4
–5
–6
–7
y
b. ,
f
f–1
12345678x
1
–1
–2
–3
–4
–5
–6
–7
y
d. ,
f
f–1
12345678x
1
2
3
4
5
6
7
8
y
Stewart – Calculus 8e ET Chapter 1 Form D
____ 7. Find the exact value of the given expression.
sin
a.
b. 0
c.
d. 1
____ 8. Simplify the expression.
a. 12
b. 36
c. 8
d. 64
____ 9. 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.
Stewart – Calculus 8e ET Chapter 1 Form D
____ 10. 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.
____ 11. If , find and simplify , where .
a.
b.
c.
d.
Stewart – Calculus 8e ET Chapter 1 Form D
____ 12. Find the domain and sketch the graph of the function. What is its range?
f (x) =
a. D: (– , ); R: (– , 0] (8, )
123456789–1 x
1
2
3
4
–1
–2
–3
–4
–5
–6
y
c. D: (– , ); R: (– , )
12345678–1–2 x
1
2
3
4
5
6
7
8
9
–1
y
b. D: (– , ); R: [0, )
12345678910x
1
2
3
4
5
6
7
8
9
10
y
d. D: (– , ); R: [–1, )
12345678–1–2 x
1
2
3
4
5
6
7
8
9
–1
y
Stewart – Calculus 8e ET Chapter 1 Form D
____ 13. The graph of the function is given. State the value of .
a.
b.
c.
d.
e.
Stewart – Calculus 8e ET Chapter 1 Form D
____ 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.
____ 15. 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
Stewart – Calculus 8e ET Chapter 1 Form D
____ 16. Graph the function by hand, not by plotting points, but by starting with the graph of one of the
standard functions and then applying the appropriate transformations.
a.
12345–1–2–3–4–5 x
1
2
3
4
5
–1
–2
–3
–4
–5
y
c.
12345–1–2–3–4–5 x
1
2
3
4
5
–1
–2
–3
–4
–5
y
b.
12345–1–2–3–4–5 x
1
2
3
4
5
–1
–2
–3
–4
–5
y
d.
12345–1–2–3–4–5 x
1
2
3
4
5
–1
–2
–3
–4
–5
y
____ 17. Suppose that the graph of is given f is given. Describe how the graph of the function
can be obtained from the graph of f.
a. Shift the graph 3 units to the right and 3 units down.
b. Shift the graph 3 units to the right and 3 units up.
c. Shift the graph 3 units to the left and 3 units down.
d. Shift the graph 3 units to the left and 3 units up.
e. None of these
Stewart – Calculus 8e ET Chapter 1 Form D
____ 18. Which of the following graphs is the graph of the function?
Graph 1
12–1–2
Graph 2
1234–1–2–3–4
Graph 3
1234–1–2–3–4
a. Graph 3
b. Graph 1
c. Graph 2
Stewart – Calculus 8e ET Chapter 1 Form D
____ 19. Find the function and its domain if and .
a.
b.
c.
d.
____ 20. The graph of the function has been compressed horizontally by a factor of 2.
Find the function for the transformed graph.
a.
b.
c.
d.
Stewart – Calculus 8e ET Chapter 1 Form D
Answer Key
Stewart – Calculus 8e ET Chapter 1 Form E
____ 1. 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. Select the correct answer.
x
y
a.
b.
c.
d.
2. 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.
____ 3. Determine whether f is even, odd, or neither. Select the correct answer.
a. neither
b. odd
c. even
4. The monthly cost of driving a car depends on the number of miles driven. Julia found that in
October it cost her to drive mi and in July it cost her to drive mi. Express
the monthly cost C as a function of the distance driven d assuming that a linear relationship gives a
suitable model.
5. If and , find a function g such that .
Stewart – Calculus 8e ET Chapter 1 Form E
____ 6. The graph of the function follows. Choose the graph of
369–3–6–9 x
3
6
9
–3
–6
–9
y
a.
369–3–6–9 x
3
6
9
–3
–6
–9
y
c.
369–3–6–9 x
3
6
9
–3
–6
–9
y
b.
369–3–6–9 x
3
6
9
–3
–6
–9
y
d.
369–3–6–9 x
3
6
9
–3
–6
–9
y
Stewart – Calculus 8e ET Chapter 1 Form E
7. Sketch the graph of over one period.
8. Find the function and its domain if and .
____ 9. If a ball is thrown into the air with a velocity of , its height (in feet) after t seconds is given
by
.
Find the velocity when Select the correct answer.
a. ft/s
b. ft/s
c. ft/s
d. ft/s
e. ft/s
10. The position of a car is given by the values in the following table.
(seconds) 0 1 2 3 4
(meters) 0 21.9 25.8 69.2 92.2
Find the average velocity for the time period beginning when and lasting 2 seconds.
____ 11. Find the value of . Select the correct answer.
.
a.
b.
c.
d.
e.
12. Find the vertical asymptotes of the function.
Stewart – Calculus 8e ET Chapter 1 Form E
13. Find the limit .
____ 14. Find the limit , if it exists. Select the correct answer.
a. 1
b. 3
c. 2
d. Does not exist
15. Evaluate the limit, if it exists.
16. Find the limit.
17. Determine where f is discontinuous.
____ 18. If f and g are continuous functions with
Select the correct answer.
a.
b.
c.
d.
e.