# 234 unit 3 review packet

```Name:______________________________________________Date:_____________Period:______________
Unit 3 Function Test Review
List the domain and range for each relation. Then tell if the set of ordered pairs is a
function by using a mapping diagram and explain in at least one full sentence. Use
1. a)
{( 9, 4 ),(3, 4),(5, 4)(-2, 4)}
b)
{( 5,2 ) , ( 6, 3) , ( 7, 7 ) , ( 5, 4 ) ,(9,1)}
Domain:___________________________
Domain:___________________________
Range:___________________________
Range:____________________________
Function: Yes or No
Function Yes or No
Explain:
Explain:
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List the domain and range of the set of ordered pairs. Then tell if the set of ordered
pairs is a function by graphing and explain.
2. a)
{( 0, 4 ),(3,2),(0,1),(-3,8)}
b)
{( 5, 3),(6,-5),(-2,5), ( 6, 4 )}
Domain:___________________________
Domain:___________________________
Range:___________________________
Range:____________________________
Function: Yes or No
Function Yes or No
Explain:
_________________________________________________
Explain:
________________________________________
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________________________________________
________________________________________________
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3. Given the table below. Identify the domain and range. Determine if the table
represents a function.
Domain:______________________________________
x
y
-1
4
-2
5
0
3
Range:______________________________________
1
7
-2
9
Does the table represent a function?
Circle: Yes or No
Explain your reasoning using math vocabulary. (Refer to the definition of a function in
________________________________________________________________________
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4. Express the a) domain and b) range represented in the graphs below using
interval notation. c) Explain if the graph is a function or not.
Domain:
Range:
Does the graph represent a function?
Circle: Yes or No
________________________________________________________________________
________________________________________________________________________
5. Express the a) domain and b) range represented in the graphs below using
interval notation. c) explain if the graph is a function or not.
Domain:
Range:
Does the graph represent a function?
Circle: Yes or No
________________________________________________________________________
________________________________________________________________________
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For the set of numbers, graph the set on a number line and write it in interval
notation.
6.
{x : -4 &pound; x &lt; 5orx &gt; 10}
6. ______________________________________________________________
For the set of numbers, graph the set on a number line and write it in interval
notation.
7.
all real numbers between -3 and 2, including -3 but not including 2
7. ______________________________________________________
For the set of numbers, graph the set on a number line and write it in set builder
notation.
8.
8._________________________________________________________
9. For the following functions:
f (x) = 2 - 7x
g(x) = -x 2 + 8x
h(x) = -2(x + 2) - 7
a.
Find g(-8).
c.
When will f(x) = 0?
10.
For the function f (x) = -x 2 + 4x - 2 , find f(3).
11.
f (x) = (x - 2)2 find f(-3) + f(4).
b.
Find f(7)- h(2).
12.
What is the vertical line test and how does it work?
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13. Use the vertical line test to determine if the graph is a function or not a
function.
14. For the following problems, determine if the graph represents a function. Then
identify the domain and the range. Write the
domain and range in interval notation.
a)
b)
a)Function: Circle One
b)Function: Circle One
Yes or No
Yes or No
Domain:
Domain:
______________________________
_______________________
Range:
Range:
_____________________________
__________________________
Given the functions f (x) = x 2 - 5 , g(x) = 3- x , and h(x) = -3x + 5 find:
15. f (-2)
16.
f (1)
g(4)
Given the functions f (x) = x 2 - 5 , g(x) = 3- x , and h(x) = -3x + 5 find:
17. f (g(1))
18. h(x) - g(x)
19. f (2) + g(3) + h(4)
20. g(f (-1))
21.
Is g(h(-2)) equal to h(g(-2))? Show your work to justify your response.
22. Are compositions commutative? (Remember that commutative means that the
order does not matter.) Explain.
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Given f (x) = x 2 - 5x and g(x) = 4x - 3, find:
23. f (x) - g(x)
25. f (2) + g(10)
24. g(x)ig(x)
26. You put cake batter in the oven. After 45 minutes, you take the cake out. Let f(x)
be the temperature of the cake x minutes after you placed it in the oven.
Explain the meaning of the following statements.
a. f (0) = 65
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b. f (5) &lt; f (10)
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c. f (45) &gt; f (60)
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27.
Graph the function on the given coordinate grid. Identify the characteristics
listed below. Show all work. NO CALCULATOR.
g(x) =
1
x-5
2
Type of function:________________
(be specific)
Domain:_______________________
(use interval notation)
Range:________________________
(use interval notation)
x-intercept:_____________________
y-intercept:_____________________
Graph the function on the given coordinate grid. Identify the characteristics listed
below. Show all work. NO CALCULATOR.
28. g(x) = -x + 8
2
Type of function:________________
(be specific)
Vertex:_________________________
x-intercept(s):___________________
y-intercept:____________________
Domain:______________________
(use Interval notation)
Range:_______________________
(use interval notation)
Graph on the coordinate plane (include a table with at least 5 points)
x
y
Graphing Calculator Section:
1. Graph the following on a graphing calculator and sketch the graph. Identify the key
characteristics. Write the domain and range in interval notation.
a.
h(x) = x 4 - 3x 2 - 5
Sketch:
x-intercept(s): ________________________
y-intercept: _______________________
Domain:
______________________
Range: __________________________
b.
g(x) = 3 x - 4
x-intercept: ________________________
y-intercept: _______________________
Domain:
______________________
Range: __________________________
Sketch:
c.
f (x) = x -1
Sketch:
x-intercept: ________________________
y-intercept: _______________________
Domain:
______________________
Range: __________________________
d.
f (x) = x + 2
Sketch:
x-intercept: ________________________
y-intercept: _______________________
Domain:
______________________
Range: __________________________
e.
f (x) = x 2 + 2x - 5 Sketch:
Vertex: _____________________________
x-intercept(s): _______________________
y-intercept: _______________________
Domain:
______________________
Range: __________________________
f.
g(x) = log x
Sketch:
Asymptotes: VA x = ________________
x-intercept: _______________________
Domain:
______________________
Range: __________________________
g. f (x) =
3
x-6
Sketch:
Asymptotes: VA x = ________________
SA y =__________________________
Domain:
______________________
Range: __________________________
x
h. h(x) = 4
Sketch:
Asymptote: HA y = ________________
Domain:
______________________
Range: __________________________
2. What types of functions have asymptotes? Give an example of an equation of a
function that would have an asymptote.
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3. A math test has a bonus question. The directions simply state that if you answer
increased by 7% of your score.
Let x = test score before answering the bonus questions.
a. Write a function, f (x), to represent the test score with the 5 bonus points.
b. Write the function, g (x), to represent the test score with the 7% percent of
increase.
c. Write a function h(x) to represent the test score with the test grade increased
by 7% first, followed by the 5 bonus points.
h(x)=
d. Write a function k(x) to represent the test score increased by 5 points first,
followed by a 7% increase.
k(x) =
e. If your test score is 75 and you answer the bonus question correctly, use the