Stewart – Calculus 8e ET Chapter 1 Form E
19. How would you define in order to make f continuous at ?
____ 20. Use the graph to determine where the function is discontinuous. Select the correct answer.
12345–1–2–3–4–5 x
1
2
3
4
5
–1
–2
–3
–4
–5
y
a. At 0
b. On the interval
c. At
d. At 1
Stewart – Calculus 8e ET Chapter 1 Form E
Answer Key
Stewart – Calculus 8e ET Chapter 1 Form F
____ 1. Plot the graph of the function f in an appropriate viewing window. Select the correct answer.
a.
1234–1–2–3–4 x
1
2
3
–1
y
c.
1234–1–2–3–4 x
1
2
3
–1
y
b.
5–5 x
5
–5
y
d.
5–5 x
5
–5
y
2. Plot the graph of the function f in an appropriate viewing window.
Stewart – Calculus 8e ET Chapter 1 Form F
3. Use the Law of Exponents to rewrite and simplify the expression.
____ 4. Starting with the graph of , find the equation of the graph that results from reflecting about
the line . Select the correct answer.
a.
b.
c.
d.
e.
5. Use the Law of Exponents to rewrite and simplify the expression.
____ 6. Starting with the graph of , write the equation of the graph that results from shifting 5 units
right. Select the correct answer.
a.
b.
c.
d.
e.
Stewart – Calculus 8e ET Chapter 1 Form F
____ 7. Find the inverse of f. Then sketch the graphs of f and on the same set of axes.
Select the correct answer.
,
a. ,
f = f –1
12345 x
1
–1
–2
–3
–4
–5
–6
–7
y
c. ,
f
f–1
12345678x
1
–1
–2
–3
–4
–5
–6
–7
y
b. ,
f
f–1
12345678x
1
2
3
4
5
6
7
8
y
d. ,
f = f –1
12345 x
1
2
3
4
5
y
8. Solve the equation.
Stewart – Calculus 8e ET Chapter 1 Form F
9. When a camera flash goes off, the batteries immediately begin to recharge the flash’s capacitor,
which stores electric charge given by
(The maximum charge capacity is and t is measured in seconds.) How long does it take to
recharge the capacitor to 90% of capacity if ?
____ 10. If , evaluate the difference quotient . Select the correct answer.
a.
b.
c.
d. h
e. none of these
11. A rectangle has perimeter m. Express the area of the rectangle as a function of the length
of one of its sides.
12. 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.
Stewart – Calculus 8e ET Chapter 1 Form F
13. 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
14. 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?
____ 15. Classify the function as a Polynomial function, a Rational function, an algebraic function, or other.
Select the correct answer.
a. Other
b. Algebraic
c. Rational
d. Polynomial
16. Use the table to evaluate the expression .
1 2 3 4 5 6
3 2 1 0 1 2
6 5 2 3 4 6
17. What is
, given that and ?
Stewart – Calculus 8e ET Chapter 1 Form F
____ 18. Which of the following is the equation for the function ? Select the correct answer.
a.
b.
c.
d.
e.
19. Find the function and its domain if and .
20. The graph of the function has been stretched horizontally by a factor of 2.
Find the function for the transformed graph.
Stewart – Calculus 8e ET Chapter 1 Form F
Answer Key
Stewart – Calculus 8e ET Chapter 1 Form G
1. Plot the graph of the function f in an appropriate viewing window.
2. Plot the graph of the function f in an appropriate viewing window.
____ 3. Starting with the graph of , find the equation of the graph that results from reflecting about
the line . Select the correct answer.
a.
b.
c.
d.
e.
4. Use the Law of Exponents to rewrite and simplify the expression.
____ 5. If a bacteria population starts with 100 bacteria and doubles every three hours, then the number of
bacteria after t hours is
.
When will the population reach 55,000? Round the answer to the nearest tenth.
Select the correct answer.
a. 22.3 hours
b. 27.3 hours
c. 32.3 hours
d. 37.3 hours
e. 17.3 hours
Stewart – Calculus 8e ET Chapter 1 Form G
____ 6. Find (a) for the function f and the real number a. Select the correct answer.
;
a. –2
b. –1
c. 1
d. 0
7. Find the exact value of the given expression.
sin–1
1
2
8. Use the laws of logarithms to expand the expression.
ln
____ 9. Simplify the expression. Select the correct answer.
a. 25
b. 32
c. 7
d. 10
10. If , evaluate the difference quotient .
____ 11. A rectangle has perimeter m. Express the area of the rectangle as a function of the length
of one of its sides. Select the correct answer.
a.
b.
c.
d.
e.
Stewart – Calculus 8e ET Chapter 1 Form G
12. Find the domain of the function
____ 13. 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. Select the correct answer.
a. 20
b. 35
c. 54
d.
e. 38
14. 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.
____ 15. Determine whether f is even, odd, or neither. Select the correct answer.
a. neither
b. even
c. odd
16. Find the range of the function.
17. If and , find a function g such that .
Stewart – Calculus 8e ET Chapter 1 Form G
____ 18. 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