P Conol - 4.1 Study Guide, Checkup, & Quiz
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Waiakea High School *
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MCA1040
Subject
Mathematics
Date
Nov 24, 2024
Type
docx
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Uploaded by DukeDiscoveryCoyote7
Peyton Conol | 10.17.23 - 4.1 Study Guide, Checkup, & Quiz
Page 2: Rewrite each of the following multiplication problems using exponents.
a.
7
⋅
7
⋅
7
⋅
7
⋅
7
⋅
7
❑
=
¿
7
6
b.
11
⋅
11
⋅
11
⋅
11
⋅
11
⋅
11
⋅
11
⋅
11
⋅
11
❑
=
¿
11
9
c.
9
⋅
9
⋅
9
⋅
9
⋅
9
⋅
9
⋅
9
⋅
9
❑
=
¿
9
8
Page 3: Simplify each of the following expressions.
a.
√
❑
¿
5
b.
3
√
64
¿
4
c.
4
√
16
¿
2
Write each of the following expressions with exponents.
d.
8
√
a
=
¿
a
1
8
e.
√
❑
b
1
2
f.
5
√
c
=
¿
c
1
5
Page 5:
a.
The domain of the function y
=
√
❑
is x≥
0
, while the range is y≥
0
.
b.
The domain of the function y
=
3
√
x
is (−
∞ ,
+
∞
)
, while the range is (−
∞ ,
+
∞
)
.
Page 6:
a.
If n
is an even positive integer, then both the domain and range of the function y
=
x
1
n
will be (
0,
∞
)
.
b.
If n
is an odd positive integer greater than 1, then both the domain and range of the function y
=
x
1
n
will be (−
∞ ,
+
∞
)
.
Page 7:
Circle your answers:
a.
When 10 is subtracted from the function y
=
x
1
9
to produce the function
y
=
x
1
9
−
10
, the function's graph y
=
x
1
9
is moved down to 10 units.
b.
When 7 is added to the function y
=
x
1
12
to produce the function y
=
x
1
12
+
7
, the function's graph y
=
x
1
12
is moved up by 7 units.
Page 8:
Circle your answers:
a.
When 6 is subtracted from x
in the function y
=
x
1
8
to produce the function
y
=(
x
−
6
)
1
8
, the function's graph y
=
x
1
8
is moved to the right 6 units.
b.
When 14 is added to x
in the function y
=
x
1
3
to produce the function y
=(
x
+
14
)
1
3
,
the function's graph y
=
x
1
3
is moved to the left 14 units.
Page 9:
Circle your answers:
a.
When the function y
=
x
1
2
is multiplied by 5 to produce the function y
=
5
x
1
2
, its graph y
=
x
1
2
is stretched, making it taller
.
b.
When the function y
=
x
1
11
is multiplied 1
4
to produce the function y
=
1
4
x
1
11
, its graph y
=
x
1
11
is shrunk
, making it shorter
.
Page 10: Circle your answers:
a.
When the function y
=
x
1
10
is multiplied by −1 to produce the function x
−(
¿¿
1
10
)
y
=
¿
, and when x
is multiplied by −1 to produce the function
x
¿
1
10
y
=−
¿
, different graphs appear.
b.
When the function y
=
x
1
13
is multiplied by −1 to produce the function
x
−(
¿¿
1
13
)
y
=
¿
, and when x
is multiplied by −1 to produce the function
y
=−(
x
)
1
13
, the same graphs appear.
Page 11: Could the graph below be that of the function x
+
1
¿
1
3
+
3
y
=−
¿
? Why or why not?
No, because the y-intercept would be (0, 2) not (0,4).
Answer the following questions using what you've learned from this lesson. Write your responses
in the space provided.
1. Identify the base and the exponent in the expression 10
15
.
Base: 10
Exponent: 15
2. Explain in your own words how we use exponents to signify repeated multiplication.
Exponents represent repeated multiplication, making numbers grow quickly. For example, 2 to the 3rd power means multiplying three 2's together, resulting in 8. This concept differs from multiplication, which is simply repeated addition.
3. Write the following using exponential notation:
(
5
⋅
5
⋅
5
⋅
5
⋅
5
⋅
5
⋅
5
⋅
5
⋅
5
⋅
5
)
⋅
(
7
⋅
7
⋅
7
⋅
7
⋅
7
⋅
7
⋅
7
⋅
7
⋅
7
⋅
7
⋅
7
⋅
7
⋅
7
⋅
7
)
(
5
10
)
⋅
(
7
14
)
4. Write √
❑
using exponential notation.
36
1
2
⋅
6 4
1
3
5. Sketch the graph of y
=
x
1
7
. Identify the domain and the range.
Domain: (−
∞ ,∞
)
Range: (−
∞ ,∞
)
6. Sketch the graph of y
=
x
1
8
. Identify the domain and the range.
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Domain: (
0,
∞
)
Range: (
0,
∞
)
7. Sketch the graph of y
=
5
√
(
x
−
4
)+
2
. Identify the domain and range.
Domain: (−
∞ ,∞
)
Range: (−
∞ ,∞
)
8. Sketch the graph of y
=
3
√
(
x
−
6
)−
4
. Identify the domain and range.
Domain: (−
∞ ,∞
)
Range: (−
∞ ,∞
)
9. Sketch the graph of y
=
−
3
√
(
x
+
1
)
. Identify the domain and range.
Domain: (−
∞ ,∞
)
Range: (−
∞ ,∞
)
For questions 10 - 13, use the following graph. Assume this is the graph of the function
x
+
k
¿
1
n
+
m
f
(
x
)=
a
¿
10. Is the coefficient greater than or less than zero? Explain your answer.
Less than because the graph is flipped.
11. Is the integer n
odd or even? Explain your answer.
Odd because its ^3
12. Is the constant k
greater than or less than zero? Explain your answer.
Less than because it’s on the right side of the graph. 13. Is the constant m
greater than or less than zero? Explain your answer.
Greater than because it goes up. 14. Give an example of a radical function, f
(
x
), whose domain is ¿
and whose range is ¿
. You do not need to graph the function, simply write it out.
x
−
3
¿
5
8
y
=−
¿
15. Give an example of a radical function, f
(
x
), that goes through the point (2, 4), and whose domain and range are both (−
∞ ,∞
)
. You do not need to graph the function, simply write it out.
x
+
1022
¿
1
5
y
=
¿
16. If n
√
b
=
r
, then which of the following is true?
a.
r
b
=
n
b.
b
r
=
n
c.
b
n
=
r
d.
r
n
=
b
17. If n
√
b
=
r
, then which of the following is true?
a.
b
1
n
=
r
b.
r
1
b
=
n
c.
b
1
r
=
n
d.
n
1
b
=
r
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