Math Extra Credit Assignment
Topic
Degree and General Form of a
Polynomial
Two-Sided Inequalities
Domains/Ranges
Evaluating Functions
Difference Quotient
X/Y Intercepts
Even/Odd/Neither Functions
Students
Work and Key
Kacie
Mike R
Jason
Josie/Josiah
Josie
Julie/Mike
D/Josiah/Deo/Chris
Cheyenne/Victor
Parent Functions (domains,
ranges, points)
Graph Analysis
Roberto
Increasing/Decreasing
Brenda
Relative Extrema
Anthony/Charlie
Evaluating Piecewise
Brianna/Danny/Brenda
Functions
Graphing Piecewise Functions
Write a piecewise Function
Dominique
given graph
Transformations: HS, VS,
Steven/Anthony
reflections
Arithmetic with Functions
Brianna
Composite Functions
Michelle/Brenda
Inverses of Functions
Danny
Quadratic Formula
Alyssa
Factoring
Alyssa/Michelle/Deo
Radical Equations
Dominique/Cheyenne
Fractional Exponents
Julie/Victor
Trig Identities (and Reciprocal Steven/Mike D
Trig Functions)
Trig Exact Values/Special
Roberto/Kacie
Right Triangles
Trig Graphs, Domains,
Mike R/Chris
Ranges for sine and cosine
Jack, Maria, Leah, Joe
Leaders
 If you are confused on a question, look up who did the question and ask that classmate
for help.
Degree and General Form of a Polynomial- Kacie
1. Which of the following is the general form of a polynomial?
a.
b.
c.
d.
e.
ax2 + bx + c
ax3 + bx2 + cx + d
axn + bxn-1 +cxn-2 + dxn-3 +…
anxn + an-1xn-1 +…+ a2x2 a1x + a0
The answer is not shown.
2. Which of the following is a 2nd Degree polynomial?
a.
b.
c.
d.
y=x+4
y = x3-2x2+3x-6
y = x2-x+2
y=8
3. The degree of y = 4x3 + 6x2 + 2x + 3 is
a.
b.
c.
d.
e.
One
Two
Three
Four
Five
4. The degree of (x3)(x2) is
a.
b.
c.
d.
e.
Three
Five
Two
One
The answer cannot be determined with the given information.
5. Simplify: 25 – (x + 3 - x2) and state its degree
a.
b.
c.
d.
x2 – 1x + 22, 2nd degree
-x2 – 1x + 28, 2nd degree
x2 – 1x + 22, 3rd degree
-x2 – 1x + 28, 3rd degree
Domains/Ranges- Mike R.
1) Which graph shown below has a domain of (-∞,0)U(0,∞)?
2) What is the domain of the function f(x) =
?
a. [0,∞)
b. (0,∞)
c. (-∞,∞)
d. [0,∞]
3) What is the range of f(x) = - x ?
a. (-∞,0)
b. (-∞,1)
c. (0, ∞)
d. (-∞,0]
4) Is the following relation a function: {(2.-3), (4,6), (3,-1), (6,6), (2,3)}? Pick the answer choice
that gives the correct answer and explanation.
a.
b.
c.
d.
No, because there are repeated Y-values.
Yes, because the same points are not repeated.
No, because there are 2 different Y-values for the same x-value.
Yes, because there aren’t any asymptotes.
5) What is the range of f(x) = x26-5?
a. [-5, ∞)
b. (-∞,-5]
c. (-∞,∞)
d. (26,∞)
Evaluating Functions-Jason
If F(x)=2x -5 and H(x) = 2/x Solve for the Following, including the domain of the combined
functions.
1) F(H(x))
a. (4/x)-10; Domain: all reals x  0
b. (4/x)-5; Domain: all reals x  0
c. (2/x)-5; Domain: all reals x  2
d. (4/x)-5; Domain: all reals x  4
e. the correct answer is not shown
2)H(F(x))
a. 2/(4x-5); Domain: all reals
b. 4/(2x-5); Domain: all reals x  0
2
c. 2/(2x-5); Domain: all reals x 
5
5
d. 2/(2x-5); Domain: all reals x 
2
e. the correct answer is not shown
3) If G(x)=x 3 , what is F(G(H(x)))?
a. (16/ x3) -5; Domain: all reals x  2
b. (16/ x3) -5; Domain: all reals x  0
c. (8/x 3 ) -5; Domain: all reals x  0
d. (8/x 2 ) -10; Domain: all reals x  2
e. the correct answer is not shown
4) What is G(F(x))?
a. 8 x 3 -60 x 2 +150 x ; Domain: all reals
b. 8 x 6 -60 x 4 +150 x 2 ; Domain: all reals
c. 8 x 3 -60 x 2 +150 x -125; Domain: all reals
d. 8 x 6 -60 x 4 +150 x 2 -125 x ; Domain: all reals
e. the correct answer is not shown
5) If W(x) =x2 -4, what is G(W(x))?
a. x6 -12x4 +48x2 -64; Domain: all reals
b. x6 -12x4 +48x2 -64; Domain: all reals x  0
c. x6 -12x4 +48x2 -64x; Domain: all reals
d. x 5 -12 x 3 +48 x -64; Domain: all reals
e. the correct answer is not shown
Difference Quotient- Josie
1. What is the DQ of 9x + 5?
a. 9x
b. -9
c. 9
d. 9h + x
2. What is the range of the DQ of 7x – 17?
a. [7]
b. [-∞, 7]
c. (-∞, 7)
d. (-∞, ∞)
3. What is the DQ of x2 + 5x – 8?
a. 2x – h + 5
b. 2xh + h + 5
c. X – h – 5
d. 2x + h + 5
4. What is the DQ of -3x + 7?
a. -3h
b. 3
c. -3
d. 3h
5. What Is the domain of the DQ of x2 + 8x – 4?
a. [0, ∞)
b. (-∞, ∞)
c. (0, ∞)
d. (-∞, 8]
Difference Quotient- Josiah
1) Which of the following is the Difference Quotient formula?
a) f(x-h) - f(x)
h
b) f(x-h) + f(x)
h
c) f(x+h) + f(x)
h
h
d) f(x+h) - f(x)
h
2) The difference quotient of the function f(x) = 3 - x2 - x is?
a) 2x + h + 1
c) -2x - h - 1
b) 2x2 + h + 2
d) 6x - h + 2
3) The difference quotient of the function f(x) = x2 + 2 in simplest form is?
a) 2x + h
c) 2xh + h2
h
b) x2 + xh - 64
d) x + h
4) The difference quotient of the function f(x) = x2 - 4 is?
a) 2x2 + h
c) 2x + h
b) 2x - h
d) 2x7 + h2 - 2
5) What is the domain of the difference quotient found from the function f(x) = (x2 + x + 1)?
a) (-∞,∞)
c) [0,∞)
b) (-∞, 5) U (5,∞)
d) [-∞,∞]
DQ- Jason
Calculate the Difference Quotient of the following
1. X2 -4X
a. 2x – h + 4
b. 2x + h + 4
c. 2x + h – 4
d. x + h – 4
2. X + H
a. 1
b. 2
c. 3
d. 4
X/Y Intercepts- Josie
1. What are the x and y-intercepts for the equation f(x) = x2 + x -20?
a. (-5, 0), (-4,0), (0, -20)
b. (-5,0), (4,0), (0, 20)
c. (5,0), (4,0), (0, -20)
d. (-5,0), (4,0), (0, -20)
2. What is the y-intercept for the equation f(x) = 4x2 – 9x + 7?
a. (0,7)
b. (7,0)
c. (-7,0)
d. (0,-7)
3. What are the x-intercepts of the equation f(x) = x3 + 4x2 – 5x?
a. (0,0), (5,0), (-1,0)
b. (0,0), (-5,0), (1,0)
c. (0,0), (-5,0), (-1,0)
d. (0,0), (5,0), (1,0)
4. How do you find the x-intercept(s)?
a. Factor as is
b. Set the y equal to 0
c. Set x equal to 0
d. Plug in numbers
5. If an equation is a function, how many y-intercept(s) should there be?
a. 2
b. 0
c. 1
d. 3
Even/Odd/Neither Functions- Julie
1. Which of these functions is odd?
A) f(x) = x
B) f(x) = x2 +5
C) f(x) = x3 -1
D) f(x) = 5
2. To determine if a function is even graphically, which property must the graph have?
A) Symmetry with respect to the x axis
B) Symmetry with respect to the y axis
C) Symmetry with respect to the origin
D) Symmetry with respect to the line y=x
3. The function f(x) = x2 +5 is
A) Odd
B) Even
C) Neither
D) Symmetric to the origin
4. To determine if a function is odd algebraically, what must be equivalent?
A) f(x) = -f(x)
B) –f(x) = f(-x)
C) –f(x) = f(x)
D) f(x) = f(-x)
5. The function f(x) = x3 -1 is
A) Odd
B) Even
C) Neither
D) Symmetric to the x axis
Even/Odd/Neither Functions- Mike D
1) If f(x) = 8, what kind of function is this?
a) Even
b) Odd
c) Neither
d) Quadratic
2) A function is _________ if it’s graph is symmetric with respect to the origin.
a) Even
b) Odd
c) Neither
d) Quadratic
3) The function f(m) = m3 – 2m is which kind of function?
a) Even
b) Odd
c) Neither
d) Constant
4) The function f(x) = x is a(n) ________ function.
a) Even
b) Odd
c) Neither
d) 2:1
5) Which function is even?
a) f(x) = x
b) f(x) = x2
c) f(x) = 1/x
d) f(x) = x3+9x-7
Even/Odd/Neither Functions- Josiah
1) Is the function f(x) = sec(x) even/odd/neither? And under which case?
a) Even, sec(-x) = -sec(x)
c) Odd, sec(x) = sec(-x)
b) Even, sec(x) = sec(-x)
d) Neither, -sec(x) = sec(-x)
2) Is the function f(x) = cot(x) even/odd/neither? And under which case?
a) Even, cot(x) = cot(-x)
c) Odd, cot(x) = cot(-x)
b) Neither, cot(x) = 1/(tan(x))
d) Odd, cot(-x) = -cot(x)
3) Is the function f(x) = x16+5 even/odd/neither? And under which case?
a) Odd, f(-x) = f(x)
c) Even, -f(x) = -f(x)
b) Neither, -f(x) = f(x)
d) Even, f(x) = f(-x)
4) Under which case is a function even?
a) symmetrical to y-axis
c) symmetrical to y=1
b) symmetrical to x-axis
d) symmetrical to f(-x)
5) Is the function f(x) = (sqrt(x+1)) + 5 even/odd/neither? And under which case?
a) Odd, -f(x) = f(-x)
c) Neither, f(x) ≠ f(-x), f(-x) ≠ -f(x)
b) Even, f(x) = (f-x)
d) Neither, f(x) ≠ f(-x)
Even/Odd/Neither Functions- Deo
1. Which of the following functions is even?
(a) f(x) = x³ – 3 (b) f(x) = sin x (c) f(x) = x² + 4
(d) f(x) = x³ – x
(e) none of these
2. Which of the following functions is even?
(a) f(x) = 7x³
(b) f(x) = 2x
(c) f(x) = cos x
(d) f(x) = x³ – 2
(e) none of these
3. Which of the following functions is odd?
(a) f(x) = x³ + 5x (b) f(x) = 3
(c) f(x) = - | x | – 3
(d) f(x) = 3π
(e) none of these
4.
Which of the following functions is odd?
(a) f(x) = (x – 3)³ (b) f(x) = sin x (c) f(x) = (.5)²
(d) f(x) = 3x² – 1 (e) none of these
5. Which of the following functions is neither even nor odd?
(a) f(x) = 0
(b) f(x) = x² – 1 (c) f(x) = x³ – 1
(d) f(x) = x – 2
(e) none of these
Parent Functions (domains, ranges, points) –Cheyenne
1. What is the domain of the function
a) (-
c) [
b) (0,
d)
2. Which points lie on the graph of the function
a) (0, -2)
c) (1, -1)
b) (1, 1)
d) (-2, 0)
3. If
, what is the value of f for which
a) 1
c) -1
?
?
b)
d)
4. What is the range of the function
a) (1,
c) [-4,
b) [1,
d) (-
?
5. Which function is the other reflected over the line
a) log, ln
c) log, exponential
b) quadratic, cubic
d) linear, constant
?
Parent Functions (domains, ranges, points)- Victor
1. What is the domain of the function f(x)=
a. (-∞, ∞)
b. (-∞, 0) U (0, ∞)
c. (-∞, ) U ( , ∞)
d. (-∞, ) U ( , ∞)
2. If f(x)=-1, and sin(x)=-1, what is a possible value of x?
a.
b. Π
c.
d. 2π
3. What is the domain of the function f(x)=
a. [0, ∞)
b. (-∞, - ) U (- , ∞)
?
c. (0, - ) U (- , ∞)
d. [0, - ) U (- , ∞)
4. In which quadrant(s) is the graph of f(x)=log(x) defined?
a. Quadrant I
b. Quadrant II
c. Quadrant I, III
d. Quadrant I, IV
5. Which equation below could depict exponential decay?
a.
b.
c.
d.
y=
y=
y=
y=
Graph Analysis- Roberto
Relative Extrema- Anthony
Directions: According to the graph of the function below please answer questions 1-3
Answer questions 4 and 5 according to the second graph
1. How many relative extrema are on the graph of this function?
____________
2. At what x-values do the relative minimums occur? _______________________
3. What are the relative maxima points? __________________________________
4. Is point (-8,1) a relative maximum? ______________________________________
5. Classify if the the point at x-value -2 is a relative maximum, relative minimum, or neither
________________________________________________________________________
Relative Extrema- Charlie
Directions: Using the following graph, answer questions 1 & 2.
1) What are the relative maxima of this graph?
A. 1
B. 1, 6
C. -5, 1, 6
D. -2, 2
2) What are the relative minima of this graph?
A. -2, 2
B. -2, 2, 9
C. -1, 8
D. 9
Directions: Use the following graph to answer questions 3-5.
3) When f(x) = -2, what is x?
A. -2
B. 2
C. -3
D. 3
4) What is the range of this function?
A. -6 ≤ x ≤ 6
B. -3 ≤ x ≤ 3
C. -∞ ≤ x ≤ ∞
D. -6 < x < 6
5) What is the domain of this function?
A. -6 ≤ x ≤ 6
B. -3 ≤ x ≤ 3
C. -∞ ≤ x ≤ ∞
D. -6 < x < 6
Evaluating Piecewise Functions- Brianna
1. f(x)=
-x2+2
x <-2
2x+1
-2 < x < 0
x2+2
x>0
Find:
f(5)
f(-2)
2. f(x)=
x-4
x2-9x-7
f(-4)
x>2
x<2
Find:
f(-1)
f(0)
f(2)
3.
f(x)=
3x-5
x>4
x2
x<4
Find:
f(7)
f(4)
f(-3)
4.
-3x+2
f(x)=
1/2x-4
x<2
x>2
Find:
f(1)
f(10)
5.
f(x)=
x2-4
x<3
2/3x-5
x>3
Find:
f(2)
Evaluating Piecewise Functions- Danny
f(15)
Use the figure above to answer questions 1 through 3.
1. What is the value for f(-5)?
A. 3
B. 7
C. 10
D. Undefined
E. None of these
2. What is the value for f(-1)?
A. 14
B. -23
C. -9
D. Undefined
E. None of these
3. What is the domain of this piece wise function?
A. (-∞,∞)
B. [-7,2)
C. [-7,-5) U (-5,2)
D. [-7,-5) U (-5,∞)
E. None of these
Use the figure above to answer questions 4 and 5.
4. What is the value of f(2)?
A. 2
B. 11/4
C. 13/8
D. Undefined
E. None of these
5. What is the value of f(9)?
A. 11
B. 15/4
C. 9/2
D. Undefined
E. None of these
Evaluating Piecewise functions- Brenda
1) What value is the piecewise function at when given f(-3)?
x-3
if x ≤ 5
f(x)=
- x-5 if 5<x≤9
-7
a) -
if x≥10
b) -7
c)-6
d)0
2) What value is the piecewise function at when given f(10)?
a) -7
b) undefined
c) -20
d) 10
3) What value is the piecewise function at when given f(8)?
a) 5
b) 2
c) -8
d) -17
if -1≤x<2
f(x)=
x2 +1 if 2<x≤8
4) When given f(4), what is the value of the piecewise function?
a) 7
b) 14
c) 17
d) 26
5) When given f(-1), what is the value of the piecewise function?
a)
b)
c) 8
d) 10
Write a piecewise Function given graph- Dominique
(Graphs are on a separate sheet of graph paper)
1. Which piecewise function best represents the given graph?
a.
b.
c.
d.
e.
2. What is the range of this given piecewise function?
a.
b.
c.
d.
e.
3. Which piecewise function best represents the given graph?
a.
b.
c.
d.
e.
4 .Which piecewise function best represents the given graph?
a.
b.
c.
d.
e.
5. Which piecewise function best represents the given graph?
a.
b.
c.
d.
e.
Transformations (HS, VS, reflections)- Steven
1. In the equation y  ( x  3)  3 which transformation(s) occurred from the original
equation y  x ?
a) Horizontal shift 3 left, vertical shift 3 down, reflection over the x-axis
b) Horizontal shift 3 right, vertical shift 3 down, reflection over the x- axis
c) Reflection over the x-axis
d) Reflection over the y-axis
e) Horizontal shift 3 left, vertical shift 3 down, reflection over the y-axis
2. Negating (m) in the general equation y=mx+b, the overall transformation would
a) Reflect over the x-axis
b) Reflect over the y-axis
c) Reflect about the origin
d) Not do anything
e) Shift vertically downwards, and shift horizontally to the right
3. What transformation occurs when negating the b term of the polynomial
function, y  ax 2  bx  c ?
a) Reflection over the x-axis
b) Reflection over the y-axis
c) Dilation
d) Reflection about the origin
e) Translation
4. The graph of an inverse function in relation to its original function has gone through
which transformation?
a) Reflection about the origin
b) Reflection over the x-axis
c) Reflection over the y-axis
d) Reflection over the line y = x
e) Dilation
5. Increasing the (a) term of the polynomial function y  ax 2  bx  c causes what kind of
transformation?
a) Translation
b) Dilation
c) Reflection over the x-axis
d) Reflection over the y-axis
e) Reflection about the origin
Transformations: HS, VS, reflections- Anthony
1. In a general function of f(x)+c, it is graphed as the function of f(x) shifted
a. To the right c units
c. To the left c units
b. Up c units
d. Down c units
2. What happens to the graph of f(x) = -|x| in relation to the graph of f(x) = |x|?
a. It remains the same
c. Its reflected over the x-axis
b. Its reflected over the line y = x
d. Its reflected over the y-axis
3. What is the maximum point of the parabola in a quadratic function, f(x) = a. (-4,0)
c. (0,-4)
b. (4,0)
d. (0,4)
Directions: Sketch functions 4 and 5 below; label each function
4. y = .5x -3
5. y = (x^3)-5
Arithmetic with functions- Brianna
1. Given f(x)= 2x2 + 2 find:
f(-3)
2. Given g(x)= -4x2 − 3x – 7 find:
f(6)
-4?
g(0)
g(3)
g(-4)
3. Find the Difference Quotient of f(x)= 8x2 – 6x + 2
4. Find the domain of the function f(x)= 7/ (x2 – 2x – 15) in interval notation
5. Find the x and y-intercepts of y=x3 – 16x
Composite Functions- Michelle
1. Several values of
A)4
B)1
C)
D)2
and
are shown in the table. Find
-4
-3
-2
-1
0
1
2
3
4
5
6
-5
-4
-3
-2
-1
0
1
2
3
4
5
-6
-5
-4
-3
-2
-1
0
1
2
3
4
2. Use the graphs of
(
and
to evaluate the functions:
AND
A)10,10
B)5,-5
C)0,10
D)
3. If
and
A)
,∞)
B)
,6)U(6,∞)
, find
. Also find the domain of
.
C)
,6)
D)
,3)U(3,∞)
4. Given
and
and
find,
.
A)
B)
5. Given
and
C) 2x-1, 4x-3 D)
find,
A)
B)6
C)8
D)3
Composite Functions- Brenda
Given: f(x)=
and g(x)= 6x+2
11) When given f(x) and g(x), what is f(g(2))?
a) 16
b) 23
Given: f(x)=
c) 32
d) 48
and g(x)=
12) When given f(x), and g(x), what is (g◦f)(5)?
a) 9
b) 15
c) 3
d) 6
13) When given f(x)=
and g(x)=
, what is f(g(7))?
a) 0
b) 1
c) 2
d) 3
14) When given f(x)=
a) 4
b) 12
and g(x)= x2+4, what is g(f(3))?
c) 16
d) 20
15) What is the domain of f(g(x)) when f(x)=
a)
, x≠2
b)
, x≠ -3
c)
, x≠ -4
d)
, x≠ -4,-2
and g(x)=
?
Inverses of Functions- Danny
For questions 1 and 2, determine if f(x) and g(x) are inverse functions of each other. If yes, then
choose the choice that says yes. If no, choose the correct inverse of f.
1. f(x) = x3 + 4
g(x) = ( 3√x) – 4
A. Yes
B. f-1(x) = 3√(x – 4)
C. f-1(x) = 1/ (x3 + 4)
D. f-1(x) = 1/ x3 + 4
E. f-1(x) = x3 – 4
2. f(x) = (x + 11) / 4
g(x) = 4x – 11
A. Yes
B. f-1(x) = 4 / (x + 11)
C. f-1(x) = 1 / (4x – 11)
D. f-1(x) = 1 / 4x – 11
E. None of these
3. In question 2, what would be f-1(x) if x was raised to the 2nd power?
A. f-1(x) = 4√(x) – 11
B. f-1(x) = √(4x – 11)
C. f-1(x) = √(4x) – 11
D. None of the above
4. In question 2, what would be f-1(x) if x was raised to the 1/2 power?
A. f-1(x) = 16x2 - 121
B. f-1(x) = 16x – 121
C. f-1(x) = 16x2 - 11
D. None of the above
5. f (x) = 2x2 + 9, Find f-1(x)
A. f-1(x) = √((x – 9) / 2)
B. f-1(x) = 1 / 2x2 + 9
C. f-1(x) = ((√x) / 2) – 9
D. None of these
Quadratic Formula- Alyssa
1. Find the solutions to
a. - ,
b.
,-
c. d.
e. -
,
,
,-
2. What are the solutions to
a.
?
b.
c.
d.
e. None of the above
3. What are the solutions to
?
a.
b.
c.
d.
e.
4. What are the solutions to
?
a.
b.
c.
d.
e.
5. Find the solutions to
=0
a.
b.
c.
d.
e.
Factoring- Alyssa
1. What is
a.
b.
c.
d.
e.
2. What is
a.
b.
c.
d.
factored completely?
factored completely?
e.
3. What is 27x^3 - 512y^3 factored completely?
a.
b.
c.
d.
e. None of the above
4. What is
factored completely?
a.
b.
c.
d.
e.
5. What is
factored completely?
a.
b.
c.
d.
e.
Factoring- Michelle
1. Factor! (*Hint: Use SOAP)
A)
B)
C)
D)
2. Factor completely.
A)
B) (4x-3)(16x^2+12x+9)
C)
D)
3. Factor completely.
A)
B)
C)
D)
4. Factor without showing work.
A) 3d(2
B) 2d(3
C) 2d(3
D) 3d(2
5. Factor the polynomial completely.
A)
B)
C)
D)
Factoring- Deo
6. Factored completely x³ – 125 is
(a) (x + 5)(x² + 5x + 25) (b) (x + 5)(x² – 5x – 25)
(c) (x – 5)(x² + 5x + 25) (d) (x – 5)(x² – 5x – 25)
(e) none of these
7. Factored completely 10x²y – 23xy – 5y is
(a) y(10x² – 23x – 5)
(b) y(10x² + 23x + 5)
(c) y(5x + 1)(2x – 5)
(d) y(5x – 1)(2x + 5)
(e) none of these
8. Which polynomial has factors of (9x + 3)(81x² – 27x + 9) ?
(a) 729x³ – 27
(b) 729x³ + 27
(c) (9x + 3)(x + 3)³
(d) (9x + 3)(x – 3)³
(e) none of these
9. Which polynomial has factors of (1 + x²)(1 + x)(1 – x) ?
(a) (1 + x)³
(b) (1 – x)³
(c) (x³ + 1)(1 – x)
(d) (x³ – 1)(1 + x)
(e) none of these
10. Factored completely a² + 3b² +4ab + 2ac + 6bc – 4b + 4c – 4 is
(a)
(a + 3b + 2)(a + b – 2c +2) (b) (a + 3b + 2)(a + b +2c +2)
(c) (a + 3b + 2)(a + b – 2c – 2) (d) (a + 3b + 2)(a + b +2c – 2)
(e) none of these
Radical Equations- Dominique
1.
a.
b.
d.
e.
2.
a.
b.
c.
c.
9
d.
34
e.
3.
a.
b.
c.
d.
e. 𝑥=−4, 𝑥=5
4.
a.
b.
c.
d.
e.
5.
a.
b.
c.
d.
e.
Radical Equations- Cheyenne
1. Solve the equation
for a so that
a) 1.5
c) 9
b)
d)
satisfies the equation.
2. Solve for x:
a) 2.8
b) 7
c) 2
d) 1.5
3. What is the general form for the simplification of a radical equation in terms of a and b?
a)
c)
b)
d)
4. What is the solution to the following equation, solving graphically?
a)
c)
b)
d)
5. Solve:
a) -9
c) 9
b) 2
d) no solution
Fractional Exponents- Julie
6. Simplify ( 3x3/2 y3 / x2 y-1/2 )-2
A) (x2y-1/2 / 9x3/2y3)
B) (9y7 / x)
C) (x / 9y7)
D) (9x3/2y3/ x2y-1/2)
7. Simplify (5x2y-4/3z)-1
A) (3z/5x2y4)
B) (5x-2y4/3z-1)
C) (3z-1/5x-2y-4)
D) (3y4z/5x2)
8. Rewrite using negative and fractional exponents (9 /
A) 9x-4
B) 9x-1/4
C) 9x1/4
D) 9x4
9. Rewrite using radicals (x2/3y1/3)
A) x6y-4
2
B)
y
C)
2
D)
10. Simplify (243/32)4/5
A) 16/81
B) 81/16
C) 81/4
D) 4/81
)
Fractional Exponents- Victor
1. Simplify
in simplest exponential form if m=5 and n=-3
a.
∙
b.
c. x
d.
2. Solve:
a.
b.
c.
d.
3. If
a.
b.
c.
d.
4. If
a.
256
=y, what does
=
equal in terms of y?
, solve for x:
b.
c.
d.
5.
a.
b.
c.
d.
-( )=x, solve for x
342
-344
334
352
Trig Identities (and reciprocal trig functions)- Steven
1.
sin(

2
  )  tan 
sin 
a) Cotθ
1
 cot 
sin 
2.
1
tan 
b) 1
c) Tanθ
d) 0
e)
sin 2 
cos 2 
a)
3.
1
 sin   1
2
1
sin 
cos 2 
sin 3 
c) sinθ
d)
b) sin 2 
c) cot 2 
d) 1
b) cot 2 
c)
b)
sin 3 
cos 2 
e)
cos 3 
sin 2 
 sin 2 
a) cot 2 (
tan 
cot 
4.
cot 
tan 

2
)
a) tan 2 
sin 4 
cos 4 
d)
e)
tan 2 
cos 2 
1
cos 
e) 1
5. Which value is not equal to cos 2  ?
cot 2 
a) 1
sin 2 
b) 1  sin 2 
c)
 2  2 sin 2 
2
d)
3  3 sin 2 3
3
Trig Identities (and reciprocal trig functions)- Mike D
1) What quadrant does csc 8 appear in?
a) I
b) II
c) III
d) IV
2) What is the value of cosine at Cos ?
a) 1
b) ½
c)
d)
3) What is the value of sec ?
a) 2/
b) 1
c)
d)
4) Csc is 2 when sin is
a) 1
b) 2
c) ½
d)
5) Sin( ) = 0, Csc( is
e) (cosθ)(cosθ)
a)
b)
c)
d)
1
½
0
Undefined
Trig Exact Values/Special Right Triangles- Roberto
Part I. Find the exact value of each function below (simplify and rationalize if necessary):
1. cot 
a) 0
2. csc
c)
b) 1
c) 
d)
e) Undefined
2
5
4
a) 0
3. cot
3
3
b) 1
3
2
d)  2
e) Undefined
7
4
a) 0
b)
2
2
c) -
2
2
d) -1
e) Undefined
Part II. Find the exact value of  for each (rationalize if necessary).
2
60°
4. cos 
a)

3
3
2
b)
2
5. csc 
a) 0
b)
2 3
3
3
c) 2
c) 1
1
Trig Exact Values/Special Right Triangles- Kacie
7. The exact value of cos(270°) is
a.
b.
c.
d.
e.
1
-1
½
–½
0
8. Given the following right triangle, what is the measure of side length x?
a.
b.
c.
d.
e.
2
2√2
2√3
3
3√2
(Questions 9 and 10) Given the following right triangle,
9. What is the length of side length u?
a.
2
b.
2√3
c.
2√2
d.
4
10. What is the length of side length v?
a.
2
b.
2√3
c.
2√2
Trig Graphs, Domains, Ranges for sine and cosine- Mike R
6) What is the range of f(x) = 2sinx?
a. [-2,2]
b. (-∞,∞)
c. (-∞,2)
d. [-1,1]
7) What is the domain of f(x) = cosx?
a. (-∞,∞)
b. [-1,1]
c. [-  , ]
d. (-1,1)
8) What is the Y-intercept of f(x) = -cosx?
a. (1,0)
b. (0,1)
c. (0,-1)
d. (-1,0)
9) What are the X-intercept(s) of f(x) =sinx? (-2≤x≤2

a. {-1,1}
b. {-

c. {-2

d. {-2
d.
4
10) Which graph shown below is the graph of f(x) = -sinx?
Mixture of Even/Odd/Neither and Trig Graphs- Chris
1. What is the domain, in interval notation, of the graph of the equation 3sinx-4?
a. (-∞, 3)U(3, ∞)
b. (-∞,∞)
c. (-4,-2)
d. (-∞, -4)U(-2, ∞)
2. The graph of the equation y=2x^2+5x+3 is
a. Even
b. Negative
c. Odd
d. Neither
3. What is difference between the relative maximum and the relative minimum of the graph
y=sinx?
a) 1
b) -1
c) 0
d) None of the above
4. Which of the following graphs is Even?
a) y=lxl-2
b) y=lx-2l
c) y=x
d) none of the above
5. On which of the following intervals is the graph of y=cosx increasing?
a) (0,π/2)
b) [0, π/2]
c) (π, 2 π)
d) [π, 2 π]
6. Which of the following graphs is Odd?
a) y=x
b) y=lxl
c) y=x^2
d) y=5
7. On which of the following intervals is y=sinx decreasing?
a) [π/2, π]
b) (π/2, π)
c) (0, π/2)
d) [0, π/2]
8. The graph of the equation y=2x-3 is
a) Even
b) Odd
c) Neither
d) None of the above
9. Which of the following is a relative maximum of the graph y=cosx?
a) (1,1)
b) (π/2,0)
c) (0,1)
d) (π/1)
10. The graph of y=x^3 is
a) Even
b) Odd
c) Neither
d) None of the above