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
proper vocabulary in your answer.(Refer to the definition of a function.)
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:
_________________________________________________
________________________________________
_________________________________________________
________________________________________
_________________________________________________
________________________________________
________________________________________________
_______________________________________
_______________________________________________
________________________________________
______________________________________________
________________________________________
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:
________________________________________
_________________________________________________
________________________________________
_________________________________________________
________________________________________
________________________________________________
_______________________________________
_______________________________________________
________________________________________
______________________________________________
________________________________________
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
your answer)
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
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
Explain your reasoning.
________________________________________________________________________
________________________________________________________________________
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
Explain your reasoning.
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
For the set of numbers, graph the set on a number line and write it in interval
notation.
6.
{x : -4 £ x < 5orx > 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?
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
________________________________________________________________
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
________________________________________________________________________________________
________________________________________________________________________________________
b. f (5) < f (10)
________________________________________________________________________________________
________________________________________________________________________________________
c. f (45) > 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
the question correctly you will receive 5 bonus points and your test grade will be
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
function h(x) to calculate your final grade.
f. If your test score is 75 and you answer the bonus question correctly, use the
function k(x) to calculate your final grade.
g. Your math teacher gives you the option of calculating our final grade using
h(x) or k(x); which would you chose? Explain.