Right Triangles
Trigonometry
Linear & Quadratics
Polynomials
Functions
Rational Functions
Sine & Cosine Graph
Inverse Functions
Equations
100
Ratios of sine, cosine, and tangent
What is
sin = (opposite)/(hypoten use) , c o s i n e = (adjacent)/(hypoten use) , tangent = (opposite)/(adjacent)
100
Period, phase shift, and amplitude of
f(x) = -4sin(4(x-pi/2))+7
What is
period = pi/2, phase shift = pi/2 to, amplitude = 4
100
Find the length and slope of the segment that connects (7,3) and (13, 7).
What is
l=sqrt(52) , m=3/2
100
Apply the Rational Root Theorem
P(x) = 7x^17+sqrt5x^6-x^3+4x^2-8x+6
What is
±1/1,±1/7, ±2/1. ±2/7, ±3/1, ±3/7, ±6/1,±6/7
100
Two key points of
h(x)=e^x
What is (0,1) & (1, e)
100
Rational Functions may have what type of asymptotes?
What is Horizontal, Vertical, and Oblique Asymptotes
100
What is the starting point of sin(x) and what is the starting point of cos(x)?
What is (0,0) & (0,1) respectively
100
To have an inverse function, a function must be a one-to-one correspondence. To fulfill this requirement, the graph needs to pass what test?
What is the horizontal line test
100
For which two type of functions may we encounter extraneous solutions and need to check our answers?
What is radical and rational functions
200
If
sin=3/8, tan= 3/6
, what is cosine?
What is
cos = 6/8
200
Find the radius of a circle if a central angle of 20° intersects an arc of length
pi/2 units
What is r = 4.5
200
Find the x-intercept, y-intercept, and slope:
8x - 6y = 24
What is
x: (3,0), y: (0,-4), m=4/3
200
If P(x) is a polynomial with zeros at
x=2, x=-sqrt(15), x=4+2i
, what is its minimal degree and what other zeros do we know about?
What is
D=5, x=sqrt(15), x=4-2i
200
Amount on deposit after 100 years if $2,000 is invested at 5% interest compounded quarterly and no other deposits are made.
What is
2,000xx(1+.05/4)^(4xx100), $287,768.17
200
State an example of a rational function with a horizontal asymptote and two vertical Asymptotes
Answers will vary.
200
What is the amplitude, period, and phase shift of the following
-3sin(2(x-pi/2))
What is amplitude = 3, phase shift =
pi/2 units
, and period =
pi units
200
To find an inverse function, what is the first step one should take?
What is switching x and y
200
Solve the following:
2/x=1/(x+2)
What is x = -2
300
Find
bar (BC)
What is
approx 5
300
Find c
What is
c approx 6.7
300
Equation of the line through (2, 3) and perpendicular to 2x + y = 10
What is
y-3=1/2(x-2)
300
Degree, Leading Coefficient, constant, and end behavior of
f(x) = -2(x-2)(x+1)(x+2)(x-1)
What is
D=4, LC=-2, C=-8, Tails: l=downarrow, r=downarrow
300
Find f(-3) and f(30) if 
What is
f(-3) = -7
f(30) = 9
300
What are the zeros & the horizontal asymptote of
(x+3)/(x^2+2x-3)
What is (-3, 0) & y=0
300
Write the function of a trigonometric curve that has an amplitude of 5, a period of 4π, and a phase shift of π/3?
Answers will vary.
300
Find the inverse function of
f(x)=4x-9
What is
f^-1(x)=(x+9)/4
300
Solve the following:
sqrt(x+3)=4
What is
x=13
400
Find
angle A
What is
angleAapprox53.1°
400
Find b
What is
bapprox9.8
400
Factored Form and zeros of
y=x^2+5x-14
What is
y=(x-2)(x+7), x=2,-7
400
Zeros of
P(x)=(x-2)^5(x+8)^6
and behavior at those zeros
What is
x=2 rightarrowcrosses, x=-8rightarrowt ouches&turns
400
Evaluate for x = -3.25 if
f(x) = abs(x-2)+3
g(x) = [x]
What is
f(-3) = 8.25
g(-3) = -4
400
What are the vertical asymptotes and holes (if any) of
(x+3)/(x^2+2x-3)
What is hole at x = -3 and V.A. at x = 1
400
Graph the following:
2cos(2(x-pi))
What is
400
Find
cos(tan^-1(4/3))
What is
3/5
400
Solve the following:
e^(2x-3)=7
What is
(ln(7)+3)/2
500
From the top of a 180ft cliff, the angle of depression to the base of a lighthouse is 22°. How far is the lighthouse from the base of the cliff?
What is
approx 445.5ft
500
Find
theta
if the angle is in standard position and the terminal ray passes through (-7, -9).
What is
theta approx 232.1°
500
Vertex Form, Vertex, and Classification of Maximum/Minimum of
4x^2-16x+18
What is
y=4(x-2)^2+2, Mi n: (2, 2)
500
Divide
3x^3-4x^2+5x-7
by
x^2-2
What is 3x-4 R11x-15
500
Graph:
f(theta) = 3sin(theta -pi/2)
What is
500
Determine whether the following has a horizontal asymptote, oblique asymptote, or neither. If it has an asymptote, find it.
(x-2)/(2x^2+4x-7)
What is y=2x+8
500
Graph the following:
-sin(4(x-pi/4))
What is
500
Find all angles between 0 and 360 degrees, such that
cos^-1(x)=0.5
What is 60 and 300 degrees
500
Solve the following:
sqrt(x+5)+sqrt(x)=5
What is x = 2