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Math 2312
Homework 5
Due: Wednesday, June 30, 2010, at the beginning of class
1.
a) Sketch the function
x
x
f
2
3
1
)
(
by first sketching the parent function and then sketching each transformation leading to
f
(
x
).
Solution:
(0,1)
(2,1)
(2,1)
(2,1)
(2,0)
x
y
3
x
y
2
3
x
y
2
3
x
y
2
3
x
y
2
3
1
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Note that the horizontal asymptote is y = 1 and the point at location (0,1) on the parent
function
x
y
3
has moved to (2,0) on the final graph.
b) State the domain and range of
f
(
x
) in interval notation.
Solution:
From the last graph, the domain is
)
,
(
(the graph extends forever to the left as well as the right, although it extends to the left very
“slowly.”
From the last graph, the range includes all values of y below the horizontal asymptote, or
)
1
,
(
2.
Solve
x
x
2
1
4
3
2
2
Solution:
The strategy would be to match the bases here:
2
,
3
0
)
2
)(
3
(
0
6
6
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This note was uploaded on 10/07/2010 for the course MATH 2312 taught by Professor Garrett during the Summer '10 term at Richland Community College.
 Summer '10
 Garrett
 Math, Calculus

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