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117 Cards in this Set

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A (larger/smaller) slope equates to a steeper line tilt.
Larger
A (positive/negative) slope equates to an upward tilt.
Positive
A (larger/smaller) slope equates to a shallower line tilt.
Smaller
A (positive/negative) slope equates to a downward tilt.
Negative
Given points (X1, Y1) and (X2, Y2) on a plane with a single line running through both of them, what is the equation to find the slope of the line.
m = (y2 - y1) / (x2 - x1)
What is the equation of a line in slope-intercept form?
y = mx + b
In the line equation y = mx + b, what does m represent?
Slope
In the line equation y = mx + b, what does b represent?
Y-intercept
What is the equation of a line in point-slope form?
y - y1 = m(x - x1)
Two lines are parallel if their slopes are ____ or both are ____.
Equal, vertical
Two lines are perpendicular if their slopes are ____.
Negative reciprocals.
A function is a special relation where ____ element(s) of Set A is/are paired with ____ element(s) of Set B.
Every, exactly one
Functions containing no variables.
Constant functions
The domain of a function from Set A to Set B is ____.
All of Set A
The range of a function from Set A to Set B is ____.
All or part of Set B
A graph must pass the ____ to be considered a function.
Virtual line test
What is the virtual line test?
Any vertical line can touch the graph either once or not at all.
A graph's horizontal extension shows the function's (domain/range).
Domain
A graph's vertical extension shows the function's (domain/range).
Range
When plotting points on a graph, (open/closed) dots should be used for values that include the dot.
Closed
When plotting points on a graph, (open/closed) dots should be used for values that do not include the dot.
Open
A graph has x-axis symmetry if ____.
f(x) = 0
A graph has y-axis symmetry if ____.
f(x) = f(-x)
A graph has symmetry with respect to origin if ____.
f(x) = -f(x)
a(-x)^y

If y is an even power this is equivalent to ____.
a(x)^y
a(-x)^y

If y is an odd power this is equivalent to ____.
-ax^y
f + g(x) can be rewritten as ____.
f(x) + g(x)
f - g(x) can be rewritten as ____.
f(x) - g(x)
fg(x) can be rewritten as ____.
f(x)g(x)
(f/g)(x) can be rewritten as ___.
f(x) / g(x)
f o g(x) can be rewritten as ____.
f( g(x) )
A function has an inverse if it ____.
Passes the horizontal line test
For inverses f(x) and f^-1 (x), if f(x) contains the point (a,b) then f^-1 (x) will contain the point ____.
(b,a)
How do you find the inverse of f(x)?
Replace f(x) with x, replace x with y, and solve for y. Replace y with f^-1 (x).
Function f(x) has identity i(x) if ____.
f o i(x) = f(x)
A quadratic function has a minimum function if the graph opens ____.
Up
A quadratic function has a maximum function if the graph opens ____.
Down
On a graph of a polynomial function, the leading coefficient is positive and the polynomial degree is even. How will the graph behave?
Both ends will point up
On a graph of a polynomial function, the leading coefficient is positive and the polynomial degree is odd. How will the graph behave?
The graph will go down and then up.
On a graph of a polynomial function, the leading coefficient is negative and the polynomial degree is even. How will the graph behave?
Both ends will point down.
On a graph of a polynomial function, the leading coefficient is negative and the polynomial degree is odd. How will the graph behave?
The graph will go up and then down.
The Rational Zero Theorem states that if p/q is a zero, then p is a divisor of the ____ and q is a divisor of the ____.
Constant term, leading coefficient
Descartes' Rule of Signs states that the maximum positive zeros in f(x) is ____.
The number of sign changes in f(x)
Descartes' Rule of Signs states that the possible positive zeros in f(x) is ____.
The maximum positive zeros minus an even whole number.
Descartes' Rule of Signs states that the maximum negative zeros in f(x) is ____.
The number of sign changes in f(-x).
Descartes' Rule of Signs states that the possible negative zeros in f(x) is ____.
The maximum negative zeros minus an even whole number.
The Upper and Lower Bounds Theorem states that the results of doing synthetic division can determine if the divisor is a bound.

How can you determine if the divisor is an upper bound?
The bottom row of the division will all be non-negative.
The Upper and Lower Bounds Theorem states that the results of doing synthetic division can determine if the divisor is a bound.

How can you determine if the divisor is a lower bound?
The bottom row of the division will alternate between non-positive and non-negative.
How many y-intercepts does every polynomial function have?
One
What is a rational function?
A function that can be written as one polynomial divided by another.
What is a vertical asymptote?
A break in the graph of a rational function where the denominator equals 0.
How do you find the y-intercept of a rational function?
By setting x to 0.
Where is the horizontal asymptote in the graph of a rational function where the degree of the numerator is larger than the degree of the denominator?
There is no horizontal asymptote.
Where is the horizontal asymptote in the graph of a rational function where the degree of the numerator is smaller than the degree of the denominator?
y = 0
Where is the horizontal asymptote in the graph of a rational function where the degree of the numerator equals the degree of the denominator?
y = a_n / b_m

a_n = leading coefficient of the numerator
a_m = leading coefficient of the denominator
How do you find the x-intercepts of a rational function?
By setting the numerator to 0.
What is the formula for calculating compound interest? Define all variables.
A = P(1 + r/n)^nt

P = Dollars invested
r = Yearly rate
n = Periods per year
t = Time in years
What is the formula for continuous compounding? Define all variables.
A = Pe^(rt)

P = Dollars invested
e = Euler's number
r = Yearly rate
t = Time in years
What is the formula for general growth? Define all variables.
n(t) = n_0 e^(rt)

n = compounding periods
t = time
n_0 = beginning amount
r = rate
What is the formula for general decline? Define all variables.
n(t) = n_0 e^(-rt)

n = compounding periods
t = time
n_0 = beginning amount
r = rate
Rewrite log_a x = y in exponential form.
a^y = x
Rewrite a^y = x in logarithmic form.
log_a x = y
Rewrite log_a a^x.
x
Rewrite a^(log_a x).
x
Rewrite the nth root of a^m?
a^(m/n)
Rewrite a^(m/n).
nth root of a^m
Rewrite 1/(a^m).
a^(-m)
Rewrite a^(-m).
1/(a^m)
Rewrite log_3 (x+1) = 4 in exponential form.
3^4 = x+1
If there are logs in both sides of an equation, when do they cancel?
When their bases are the same.
In log_x a, what must a be?
a > 0
Rewrite log_b mn.
log_b m + log_b n
Rewrite log_b m + log_b n.
Log_b mn
Rewrite log_b (m/n).
log_b m - log_b n
Rewrite log_b m - log_b n.
log_b (m/n)
Rewrite log_b m^t.
t log_b m
Rewrite t log_b m.
log_b m^t
What is the change of base formula for logarithm log_b x? Let a equal the new base.
log_b x = (log_a x) / (log_a b)

b = old base
a = new base
How do you solve an equation when exponents with variables are on both sides?
1. Take log or ln of each side.
2. Use log property three to remove exponents from logs.
3. Move x to one side.
4. Factor x.
5. Divide to isolate x.
What are two ways to solve systems of equations?
Substitution and elimination by addition.
If two systems of equations do not yield an intersection, what might they be? How do you determine which is correct?
Parallel or the same line. If the result is true, it is the same line. If the result is false, they are parallel.
What is the memory aid for the right-angle trigonometry function?
SOHCAHTOA

Some
Old
Helmets
Can
Allow
Head
Trauma
On
Accidents

Sin = Opposite / Hypotenuse
Cosine = Adjacent / Hypotenuse
Tangent = Opposite / Adjacent
Reproduce the unit circle memory aid for sin, cos, tan, sec, and csc.
tan is sin/cos
sec is 1/cos
cot is cos/sin
csc is 1/sin
Where is the unit circle centered?
The origin
What is the radius of the unit circle?
1
What are the two sides of an angle?
Initial side and terminal side
Which direction do positive angles rotate?
Counter-clockwise
Which direction do negative angles rotate?
Clockwise
What are radians based on?
The circle's circumference
What is the circumference of a unit circle?
2pi
How many radians is a 360 degree circle?
2pi radians
How many radians is a 180 degree circle?
pi radians
What are the three instances in which an angle can be co-terminal?
Terminal sides are identical

Difference between angles is a multiple of 360 degrees

Difference between angles is a multiple of 2pi
How many radians are in one degree?
pi/180
How many degrees are in one radian?
180/pi
What does theta's reference angle represent?
The smallest angle between the terminal side of the angle and the x-axis
How are the quadrants numbered?
II I
III IV
For angle theta, the point where the terminal side intersects the circumference of the unit circle, how do you determine (x,y)?
x = cos theta
y = sin theta
What is the equation of the unit circle?
x^2 + y^2 = 1
In which quadrants of the unit circle is cosine positive?
I and IV
In which quadrants of the unit circle is cosine negative?
II and III
In which quadrants of the unit circle is sine positive?
I and II
In which quadrants of the unit circle is sine negative?
III and IV
For what range of x is y positive on the graph of f(x) = sin x?
0 through pi
For what range of x is f(x) negative on the graph of f(x) = sin x?
pi through 2pi
For what range of x is f(x) positive on the graph of f(x) = cos x?
3pi/2 through 2pi + pi/2
For what range of x is y negative on the graph of f(x) = cos x?
pi/2 through 3pi/2
What translation occurs between f(x) = cos x and f(x) = sin x?
The graph is shifted pi/2 units horizontally
How are f(x) = c + sin x and f(x) = c + cos x translated in relation to c?
They are shifted up c units
How are f(x) = c sin x and f(x) = c cos x translated in relation to c?
They are stretched by a factor of c
How are f(x) = sin (x - c) and f(x) = cos (x - c) translated in relation to c?
They are shifted horizontally by c units
In a sine or cosine transformation, the degree of vertical stretching or compressing.
Amplitude
In a sine or cosine transformation, the horizontal shift.
Phase shift
Write the identities of the right-angle trigonometric functions.
sin = O/H
cos = A/H
tan = O/A
cot = A/O
sec = H/A
csc = H/O
When can trigonometric functions have inverses?
When their domain is limited
What are two names for the inverse of sin?
arcsin and sin^-1
Rewrite arcsin theta = x to find the value of theta.
sin x = theta