6 Chapter Test
Do you know HOW?
Simplify each radical expression. Use absolute value symbols when needed.
-
54
x
3
y
5
square root of 54 , x cubed , y to the fifth end root
-
−
0.027
3
cube root of negative , 0.027 end root ,
-
−
64
x
14
y
20
5
the fifth , root of negative 64 , x to the fourteenth . y to the twentieth end root ,
Simplify each expression. Rationalize all denominators.
-
7
x
3
⋅
14
x
square root of 7 , x cubed end root , dot , square root of 14 x end root
-
1
−
3
x
6
x
fraction 1 minus , square root of 3 x end root , over square root of 6 x end root end fraction
-
48
+
2
27
+
5
12
square root of 48 plus 2 square root of 27 plus 5 square root of 12
-
(
3
+
2
5
)
(
1
−
20
)
open . 3 plus 2 square root of 5 . close . open , 1 minus square root of 20 , close
-
4
7
x
z
+
2
7
x
z
4 , square root of 7 x z end root , plus 2 , square root of 7 x z end root
-
5
2
7
−
2
fraction 5 square root of 2 , over square root of 7 minus square root of 2 end fraction
Simplify each expression.
-
(
125
)
−
2
3
open 125 close super negative , 2 thirds end super
-
x
1
6
⋅
x
1
3
x super 1 sixth end super , dot , x super 1 third end super
-
(
8
x
9
y
3
27
x
2
y
12
)
2
3
open . fraction 8 , x to the ninth , y cubed , over 27 , x squared , y to the twelfth end fraction . close super 2 thirds end super
-
8
x
5
−
18
x
5
square root of 8 , x to the fifth end root , minus . square root of 18 , x to the fifth end root
Solve each equation. Check for extraneous solutions.
-
x
−
3
=
x
−
5
square root of x minus 3 end root , equals x minus 5
-
x
+
4
=
3
x
square root of x plus 4 end root , equals , square root of 3 x end root
-
2
(
x
−
1
)
3
4
=
16
2 . open , x minus 1 , close super 3 fourths end super . equals 16
-
x
+
3
−
1
=
x
square root of x plus 3 end root , minus 1 equals x
Let
f
(
x
)
=
x
−
2
f open x close equals x minus 2 and
g
(
x
)
=
x
2
−
3
x
+
2
.
g open x close equals , x squared , minus 3 x plus 2 . Perform each function operation and then find the domain.
-
−
2
g
(
x
)
+
f
(
x
)
negative 2 g open x close plus f open x close
-
−
f
(
x
)
·
g
(
x
)
negative f open x close middle dot g open x close
-
g
(
x
)
f
(
x
)
fraction g , open x close , over f , open x close end fraction
Find each product or quotient.
-
5
(
5
4
)
square root of 5 . open , the fourth , root of 5 , , close
-
x
3
x
2
5
fraction square root of x cubed end root , over the fifth , root of x squared end root , end fraction
For each pair of functions, find (
g
∘
f
)
(
x
)
g composition f close open x close and
(
f
∘
g
)
(
x
)
.
open f composition g close open x close .
-
f
(
x
)
=
x
2
−
2
,
g
(
x
)
=
4
x
+
1
f open x close equals , x squared , minus 2 comma g open x close equals 4 x plus 1
-
f
(
x
)
=
2
x
2
+
x
−
7
,
g
(
x
)
=
−
3
x
−
1
f open x close equals , 2 x squared , plus x minus 7 comma g open x close equals negative 3 x minus 1
Find the inverse of each function. Is the inverse a function?
-
f
(
x
)
=
(
x
+
3
)
2
+
1
f open x close equals . open x plus 3 close squared . plus 1
-
f
(
x
)
=
2
x
+
1
f , open x close , equals . square root of 2 x plus 1 end root
-
g
(
x
)
=
3
x
3
−
4
g open x close equals , 3 x cubed , minus 4
-
f
(
x
)
=
1
4
x
f , open x close , equals , 1 fourth , x
Rewrite each function to make it easy to graph using transformations. Describe the graph.
-
y
=
16
x
+
80
−
1
y equals . square root of 16 x plus 80 end root . minus 1
-
y
=
9
x
+
3
y equals . square root of 9 x plus 3 end root
Graph. Find the domain and range of each function.
-
y
=
2
x
+
3
y equals 2 square root of x plus 3
-
y
=
−
2
x
+
3
y equals negative . square root of 2 x plus 3 end root
-
y
=
x
+
3
−
4
y equals , square root of x plus 3 end root , minus 4
Do you UNDERSTAND?
-
Writing Explain why
−
108
negative 108 has no real 6th roots.
-
Open-Ended Write a relation that is not a function, but whose inverse is a function.
-
Measurement The time t in seconds for a swinging pendulum to complete one full cycle is given by the function
t
=
0.2
l
,
t equals 0.2 , square root of l comma where l is the length of the pendulum in centimeters. To the nearest tenth, how long is a full cycle if the pendulum is 10 cm long? 20 cm long? How long, in centimeters, is a pendulum that takes 2 seconds for one full cycle?
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