Name _________________________________ MPS21 Date
REVIEW FOR EXAM # 2 (Complete the work on a separate sheet of looseleaf)
1) Determine, algebraically, if the 2) Determine, algebraically, if the 3) Determine, algebraically, if the
following function is even, odd, or neither. following function is even, odd, or neither. following function is even, odd, or neither.
(SHOW ALL WORK!) (SHOW ALL WORK!) (SHOW ALL WORK!)
!(#) = −3# ! − 5 !(#) = 3# " − # ! !(#) = −# #
4) Determine, algebraically, if the 5) Determine, algebraically, if the 6) Determine, algebraically, if the
following function is even, odd, or neither. following function is even, odd, or neither. following function is even, odd, or neither.
(SHOW ALL WORK!) (SHOW ALL WORK!) (SHOW ALL WORK!)
3 !(#) = −2# !(#) = # #
!(#) =
#$
7) Determine, algebraically, if the 8) Determine, algebraically, if the 9) Is the following relation a function?
following function is even, odd, or neither. following function is even, odd, or neither.
(SHOW ALL WORK!) (SHOW ALL WORK!) {(−3, −3), (−2, −2), (−1, −1), (0,0)}
!(#) = 5# + 1 !(#) = |2#|
10) Is the following relation a 11) Is the following relation a 12) Is the following relation a
function? function? function?
{(3,4), (3,5), (4,4), (4,5)} - ! + / ! = 25 -/ + 2/ = 1
13) Are the following relations a 14) Are the following relations a 15) State the domain of the function
function? function? %&!
!(#) =
a) b) √%()
a) b)
16) State the domain of the function 17) State the domain of the function 18) Given: / = {1, 3, 4} and 6 =
*
!(#) = #%(! !(#) = √2# + 4 {0,1,2,3}, determine which of the
following represents a function from A
to B?
(a) {(1, 1), (4, 2), (4, 3), (3, 3)}
(b) {(1, 1), (3, 2), (4, 3)}
(c) {(1, 1), (0, 1), (2, 4), (3, 3)}
(d) {(4, 0), (3, 0), (1, 3)}
19) Which set of ordered pairs 20) Which of the following are 21) Which of the following are
represents a function from A to B? functions: functions:
/ = {10,20,30,40} and B= {0,2,4,6}
a) 9 = |#| a) 16# ! − 9 ! = 0
(a) {(20,4), (40,0), (20,6), (30,2)} b) 29 + # = 3 b) 29 + # ! = 8
(b) {(10,4), (20,4), (30,4), (40,4)} *
c) 9 = c) 9 = √2# + 3
"(#%
(c) {(40,0), (30,2), (20,4), (10,6)} d) 2 + 9 # = #
d) |9| = #
(d) {(20,2), (10,0), (40,4)}
22) State the equation and sketch the 23) State the equation and sketch the 24) State the equation and sketch the
graph of the identity function. graph of the Squaring function. graph of the Cubing function.
25) State the equation and sketch the 26) State the equation and sketch the 27) State the equation and sketch the
graph of the Absolute value function. graph of the Square root function. graph of the reciprocal function.
28) State the equation and sketch the 29) State the equation and sketch the 30) State the equation and sketch the
graph of the Greatest Integer function. graph of the Natural Exponential graph of the Natural Log function.
function.
31) How many x-intercepts would the 32) How many x-intercepts would the 33) How many x-intercepts would the
graph of the following equation have? graph of the following equation have? graph of the following equation have?
9 = (5# + 1)(# ! + 25)(# − 7)! # − 9! = 1 0 = ## − # − 9
34) How many x-intercepts would the 35) Write the equation of the line that !%
36) Evaluate each for !(#) = > # ?
graph of the following equation have? passes through the point (3, −2) and is
a) !(1.2)
9 = −# ! + 5# + 6 perpendicular to the line 5# − 49 = 8.
b) !(−0.9)
c) !(−A)
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40) Write the definition of the piecewise 41)
function shown. Sketch the graph of a possible function/ such that 0
y
• f is an even function
• intercept at (2,0)
• relative min at (-4, -3)
• domain: [-6,0) u (0,6]
• range: [-3,5)
-•
42) A) Graph the piecewise function defined by the following:
f(x) = {-2x + 1, X::,; 2
Sx -10, x> 2
B) Evaluate each:
i) f(-3) =
=
/
ii) f (2)
iii) f (3) =
43) State the following based on the graph off shown to the right. Write 'none' if the answer cannot be found based on the graph.
(a)Domain: [-1/o) U( O/3]
(b) Range: ----=[O_,_lf_]=--- - - - -
5-'--)_ _ __
1 _0_,_)_U_.c.(_2_.1'--
(c) Increasing interval: ____.(_-~(1-
Decreasing interval: _...._(_0_,,._1_2_,;....)________
/V
Constant interval: _____d_/J
_________
N_t)_
(d) At what x-value is there a local maximum? _ _ /II_
<,; _ .,
At what x-value is there a local minimum? ,2
44)
State the following based on the graph off shown to the right. Write ' none' if the answer cannot be found based on the graph.
(a) Domain: [- 2; f) U( I, 1 J
(b) Range: _ _ [-_L/.,_S-=J_____
{_o--'-/_l.....,)'-----
(c) Increasing interval: _...._{_-_2_1_-1-'-)_U
__
Decreasing interval: { - I/ 0 ) U( 11 2 ) ·2
Constant interval: ·~A)(} Ill€
--~-~-------- ·2
(d) At what x-value is there a local maximum? -/ tin rJ. f
At what x-value is there a local minimum? 0
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