Test 1 #3
PreCalculus / PreCalculus MAC1140 Fall 2013 – 86885 (Mr. Budhathoki)
Student Name/ID:
1. The one-to-one function
Find
, the inverse of
2. The one-to-one function
is defined below.
. Then give the domain of
using interval notation.
is defined by
.
Find
, the inverse of
. Then, give the domain and range of
using interval notation.
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3. For each function graphed below, state whether it is one-to-one.
One-to-one?:
Yes No
One-to-one?:
Yes No
One-to-one?:
Yes No
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One-to-one?:
Yes No
One-to-one?:
Yes No
One-to-one?:
Yes No
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4. Suppose
.
Find two functions
and
such that
.
Neither function can be the identity function.
(There may be more than one correct answer.)
5. For the real-valued functions
and
, find the composition
and
specify its domain using interval notation.
Domain of
:
6. Suppose that the functions
Find
and
and
are defined as follows.
. Then, give their domains using interval notation.
Domain of
:
Domain of
:
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7. The graph of
Graph
is shown below.
.
8. Below is the graph of
.
Translate it to make it the graph of
.
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9. The graph of
graph of
(in blue) is translated a whole number of units horizontally and vertically to obtain the
(in red).
The function
is defined by
Write down the expression for
.
.
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10. Four functions are given below. Either the function is defined explicitly, or the entire graph of the function
is shown.
For each, decide whether it is an even function, an odd function, or neither.
The function
- Even - Odd - Neither
The function
- Even - Odd - Neither
- Even - Odd - Neither
- Even - Odd - Neither
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11.
Find the difference quotient
, where
, for the function below.
Simplify your answer as much as possible.
12. Find the domain of the function.
Write your answer as an interval or union of intervals.
13. Simplify. Write your answers without exponents.
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14. Determine the interval(s) on which the function is (strictly) decreasing.
Write your answer as an interval or union of intervals.
15. Sam can choose Plan A or Plan B for his long distance charges. For each plan, cost (in dollars) depends
on minutes used (per month) as shown below.
a. If Sam makes
minutes of long distance calls for the month, which plan costs less? How much
less does it cost than the other plan?
b. For what number of long distance minutes do the two plans cost the same? If the time spent on
long distance calls is less than this amount, which plan costs less?
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Test 1 #3 Answers for class PreCalculus / PreCalculus MAC1140 Fall 2013
– 86885
1.
Domain of
:
2.
Domain
Range
.
3.
4.
5.
Domain of
:
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6.
Domain of
:
Domain of
:
7.
8.
9.
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10. The function
- Odd
The function
- Neither
- Neither
- Odd
11.
12.
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13.
14.
15.
(a) If Sam makes
minutes of long distance calls for the month, which plan costs less?
Plan B
How much less does it cost than the other plan?
(b) For what number of long distance minutes do the two plans cost the same?
If the time spent on long distance calls is less than this amount, which plan costs less?
Plan A
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