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Supplemental Problems and Solutions about Functions, Exams of Algebra

Supplemental problems and solutions about functions, including finding the domain and range, evaluating functions, and solving for specific output values. It covers various types of functions, such as linear, quadratic, and piece-wise functions.

Typology: Exams

Pre 2010

Uploaded on 08/19/2009

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koofers-user-5z6 ๐Ÿ‡บ๐Ÿ‡ธ

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Mr. Simondsโ€™ MTH 65 Class - Supplemental problems about functions
Page 1 of 2
1. Suppose that
f
is the function
(
)
(
)
(
)
(
)
{
}
2, 6,5, 6, 2, 6,4, 6โˆ’โˆ’โˆ’โˆ’โˆ’.
a. What are the domain and range of
f
?
b. What is the value of
(
)
4f?
c. What is the value of
(
)
6fโˆ’?
2. Consider the function g shown in Figure 1.
a. What are the domain and range of g?
b. What is the value of
()
4g?
c. What are all of the values of
x
with the property that
(
)
0gx
=
?
3. Consider the function
f
shown in Figure 2.
a. What are the domain and range of
f
?
b. What is the value of
()
2f?
c. For what values of
x
does
(
)
2fx
=
?
4. Consider the function h shown in Figure 3.
a. What are the domain and range of h?
b. What is the value of
()
2hโˆ’?
c. For what values of
x
does
()
2hx
โˆ’?
5. Find
()
4gโˆ’ and
()
4g if
(
)
2
gx x=. 6. Find
(
)
2f and
(
)
6f
โˆ’
if
()
6fx=โˆ’
7. What is the domain of the function
()
2
25
fx x
=
โˆ’
?
()
3.2,2
Figure 1 Figure 2 Figure 3
pf2

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Mr. Simondsโ€™ MTH 65 Class - Supplemental problems about functions

Page 1 of 2

1. Suppose that f is the function { ( 2, โˆ’ 6 , 5,) ( โˆ’ 6 ,) ( โˆ’2, โˆ’ 6 , 4,) ( โˆ’ 6 )}.

a. What are the domain and range of f?

b. What is the value of f ( 4 )?

c. What is the value of f ( โˆ’ 6 )?

  1. Consider the function g shown in Figure 1.

a. What are the domain and range of g?

b. What is the value of g ( 4 )?

c. What are all of the values of x with the property that g ( x ) = 0?

  1. Consider the function f shown in Figure 2.

a. What are the domain and range of f?

b. What is the value of f ( 2 )?

c. For what values of x does f ( x ) = 2?

  1. Consider the function h shown in Figure 3.

a. What are the domain and range of h?

b. What is the value of h ( โˆ’ 2 )?

c. For what values of x does h x ( ) = โˆ’ 2?

5. Find g ( โˆ’ 4 )and g ( 4 )if g ( x ) = x^2. 6. Find f ( 2 )and f ( โˆ’ 6 )if f ( x ) = โˆ’ 6

7. What is the domain of the function f ( x ) = x โˆ’^2 25?

Figure 1 ( 3.2, 2) Figure 2^ Figure 3

Mr. Simondsโ€™ MTH 65 Class - Supplemental answers about functions

Page 2 of 2

Note: Explanations are there simply to help you understand. I do not expect you to write explanations when answering questions like this on your test!

1. a. The domain of f is { 2,5, โˆ’ 2, 4}and the range of f is { โˆ’ 6 }

b. f ( 4 )= โˆ’ 6 because one of the points in the set is ( 4, โˆ’ 6 ).

c. f ( โˆ’ 6 )is undefined because there is no point in the set with an x -coordinate of โˆ’ 6.

2. a. The domain of g is ( โˆ’โˆž โˆž, )and the range of g is ( โˆ’โˆž, 2 ].

b. g ( 4 )= 0 because one of the points on g is ( 4,0)

c. The values of x where g ( x ) = 0 are โˆ’ 3 , 2 , and 4 because the points on g with a y -

coordinate of 0 are ( โˆ’3,0 ), ( 2,0 ), and ( 4,0)

3. a. Both the domain and range of f are ( โˆ’โˆž โˆž, ).

b. f ( 2 )= 0 because one of the points on f is ( 2,0)

c. The only value of x where f ( x ) = 2 is 6 because ( 6, 2) is the only point on f with a y -

coordinate of 2.

4. a. The domain of h is [ โˆ’3, 2 )and the range of h is [ โˆ’1,5)

b. h ( โˆ’ 2 )= โˆ’ 1 because one of the points on h is ( โˆ’2, โˆ’ 1 )

c. There is no value of x^ where h x ( ) = โˆ’ 2 because none of the points on h^ have a y -

coordinate of โˆ’ 2.

5. (^ )^ (^ )

g โˆ’ = โˆ’

and (^ )^

g =

6. f ( 2 )= โˆ’ 6 and f ( โˆ’ 6 )= โˆ’ 6. If we graphed the set of points in this function, it would be the

horizontal line where all of the y -coordinates are โˆ’ 6.

7. The domain is ( โˆ’โˆž,25 ) โˆช ( 25,โˆž ). x cannot be 25 because that would lead to division by zero!

That u-ish looking symbol is called a union sign. It basically means (in this expression) that the domain consists of all numbers less than 25 and all numbers greater than 25.

The parentheses are required around โˆ’ 4 so that we square the number โˆ’ 4. Regardless of what you mean, the meaning of

โˆ’ 4 2 is โˆ’ ( 42 ), not ( โˆ’ 4 )^2.