X-coordinate of the point where a line crosses the horizontal axis
X-intercept
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Slopes of perpendicular lines
Slopes are negative reciprocals
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Point where two lines intersect
Solution to a system of equations
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Reciprocal
Multiplicative inverse
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Slope of a vertical line
The slope is undefined
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Output variables
Range
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General form
Ax+By+C=0
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Piecewise function
A function defined b two r more equations over a specified domain
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Vertical line test
Way to tell if a graph is a function visually
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Equation to find slope
M=(y2-y1)/(x2-x1)
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Domain explanation
Domain is the furthest x value to the left and right
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Range explanation
Highest and lowest y values
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Polynomial function the 0 degree is what kind of function
Constant function
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Polynomial function the 1st degree is what kind of function
Linear function
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Polynomial function the 3rd degree is what kind of function
Cubic function
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what does “n” represent in the leading coefficient test
The degree of the function
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How does the graph behave when “n” is odd and the leading coefficient is positive
Falls to the left and rises to the right
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How does the graph behave when “n” is even and leading coefficient is positive
Rises to the left and rises to the right
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How does the graph behave when “n” is odd and leading coefficient is negative
Rises to the left and falls to the right
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How does the graph behave when “n” is even and leading coefficient is negative
Falls to the left and falls to the right
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Asymptotes
Lines that a graph of a function approaches but never touches
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N(x) represents
The numerator
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D(x) represents
The denominator
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Asymptotes effect the graphs
End behavior
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If the degree of the numerator N(x) is less than the degree of the denominator D(x) the graph has a horizontal asymptote at
Y=0
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If the degree of the numerator N(x) is equal to the degree of the denominator D(x) the graph of “f” has a horizontal asymptote at where “a” and “b” are the leading coefficients of N(x) and D(x) respectively
Y=a/b
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If the degree of the numerator N(x) is greater than the degree of the denominator D(x) the graph of “f” has
No horizontal asymptote
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Multiplicity
When one answer is worth three for example X^3=0 is x=0 three times
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The imaginary unit
“i”
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quadratic formula
\
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Vertex form of parabolas
Y=a(x-h)^2+k
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what does “h” in vertex form represent
X coordinate of the vertex
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What does the “k” in vertex form represent
Y coordinate of the vertex
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formula to find the vertex of a parabola
X= -b/2a
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Axis of symmetry on a parabola
The point that divides the graph into two halves
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Formula used when compounding a certain amount of time (ex. A year)
A=P(1+r/n)^nt
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“N” value when compounded annually
1
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“N” value when compounded semiannually
2
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“N” value when compounded quarterly
4
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“N” value when compounded bimonthly
6
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“N” value when compounded monthly
12
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“N” value when compounded semimonthly
24
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“N” value when compounded bi weekly
26
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“N” value when compounded weekly
52
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“N” value when compounded daily
365
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“N” value when compounded continuously
E
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Amplitude
vertical stretch/ compression (height of one wave)
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Period
Horizontal stretch/ compression (length of one full cycle of the wave)
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Phase Shift
Horizontal shift (determine how far the graph shifts)
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Vertical shift
Shifts the graph up and down
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2pi/b is h used to find what in a sine graph
The period
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When the sine is equal to zero, the close cosecant is ___ and there will be a ____ on the graph
Undefined, asymptote
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When the cosine is equal to __the ____ is undefined and there will be an asymptote
Zero, secant
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Amplitude in a sine and cosine graph
“A” (first value)
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Amplitude in secant, cosecant, and tangent
No amplitude
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Formula used to find the period in a tangent graph
Pi/b
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Angle
Two rays with the same initial point
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Angles that measure between 0 and pi/2 (90) are
Acute
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Shared initial point of two rays
Vertex of the angle
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Angles that measure between pi/2 (90) and pi (180) are
Obtuse
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Two positive angles are said to be _______ if the sum of their angles is pi/2 (90)
Complimentary
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Two positive angles are said to be _________ if the sum of their measures is pi (180)
Supplementary
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The ____________ is the amount of rotation required to rotate to one side called the ______ to the other side called the _______
Measure of the angle, initial, terminal side
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Two angles in standard position that have the same terminal side are said to be _____
Coterminal
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To convert degrees to radians multiple degrees by
Piradians/180
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To convert radians to degrees multiply radians by
180/piradians
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One radian is
The measure of a central angle feta that intercepts an arc *s* equal in length to the radius *r* of the circle
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The radian measure of any central angle is
The length of the intercepted arc divided by the circle’s radius
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How to find a co-terminal angle
Add or subtract 360 degrees of 2pi
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Standard position
1\.) It’s vertex is at the origin of a rectangular coordinate system
2\.) It’s initial side lies along the positive x-axis
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Sine=
Y and opposite/hypotenuse
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Cosine=
X and adjacent/hypotenuse
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Tangent=
Y/x and opposite/adjacent
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cosecant=
1/y, hypotenuse/adjacent, 1/sin
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Secant=
1/x, hypotenuse/adjacent, 1/cos
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cotangent
X/y, adjacent/opposite, 1/tan
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On the Unit circle for every 30 degrees you go ___ radians
Pi/6
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On the Unit circle for every 45 degrees you go every ____ radians
Pi/4
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Y=sin^-1x
\[-pi/2, pi/2\] (Q1 and Q4)
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Y=cos^-1x
\[O, pi\] (Q1 and Q2)
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Y= tan^-1x
(-pi/2, pi/2) (Q1 and Q4)
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Pythagorean Theorem
A^2+B^2=c^2
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Angle of elevation
An angle formed by a horizontal line and the line of sight to an object that is above the horizontal line (Ex. Looking up at a kite)
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Angle of depression
The angle formed by a horizontal line and the line of sight to an object that is below the horizontal line (Ex. Lookin down from a building)
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Trigonometric Identity
An equation that is true for all values except those for which the expressions on either side of the equal sign are undefined