Studied by 32 peopleFunction Notation
A way to name and evaluate functions
Difference Quotient
F(x+h)-f(x)
—————, h=0
h
Point Slope form
Y-y1=m(x-x1)
Slope Intercept form
Y=mx+b
Slope
Rate of change
“b” in y=mx+b
Y intercept
Slope of a horizontal line
Slope=0
Standard form
Ax+by=C
Input variables
Domain
X-coordinate of the point where a line crosses the horizontal axis
X-intercept
Slopes of perpendicular lines
Slopes are negative reciprocals
Point where two lines intersect
Solution to a system of equations
Reciprocal
Multiplicative inverse
Slope of a vertical line
The slope is undefined
Output variables
Range
General form
Ax+By+C=0
Piecewise function
A function defined b two r more equations over a specified domain
Vertical line test
Way to tell if a graph is a function visually
Equation to find slope
M=(y2-y1)/(x2-x1)
Domain explanation
Domain is the furthest x value to the left and right
Range explanation
Highest and lowest y values
Polynomial function the 0 degree is what kind of function
Constant function
Polynomial function the 1st degree is what kind of function
Linear function
Polynomial function the 3rd degree is what kind of function
Cubic function
what does “n” represent in the leading coefficient test
The degree of the function
How does the graph behave when “n” is odd and the leading coefficient is positive
Falls to the left and rises to the right
How does the graph behave when “n” is even and leading coefficient is positive
Rises to the left and rises to the right
How does the graph behave when “n” is odd and leading coefficient is negative
Rises to the left and falls to the right
How does the graph behave when “n” is even and leading coefficient is negative
Falls to the left and falls to the right
Asymptotes
Lines that a graph of a function approaches but never touches
N(x) represents
The numerator
D(x) represents
The denominator
Asymptotes effect the graphs
End behavior
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
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
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
Multiplicity
When one answer is worth three for example X^3=0 is x=0 three times
The imaginary unit
“i”
quadratic formula
Vertex form of parabolas
Y=a(x-h)^2+k
what does “h” in vertex form represent
X coordinate of the vertex
What does the “k” in vertex form represent
Y coordinate of the vertex
formula to find the vertex of a parabola
X= -b/2a
Axis of symmetry on a parabola
The point that divides the graph into two halves
Formula used when compounding a certain amount of time (ex. A year)
A=P(1+r/n)^nt
“N” value when compounded annually
1
“N” value when compounded semiannually
2
“N” value when compounded quarterly
4
“N” value when compounded bimonthly
6
“N” value when compounded monthly
12
“N” value when compounded semimonthly
24
“N” value when compounded bi weekly
26
“N” value when compounded weekly
52
“N” value when compounded daily
365
“N” value when compounded continuously
E
Amplitude
vertical stretch/ compression (height of one wave)
Period
Horizontal stretch/ compression (length of one full cycle of the wave)
Phase Shift
Horizontal shift (determine how far the graph shifts)
Vertical shift
Shifts the graph up and down
2pi/b is h used to find what in a sine graph
The period
When the sine is equal to zero, the close cosecant is ___ and there will be a ____ on the graph
Undefined, asymptote
When the cosine is equal to __the ____ is undefined and there will be an asymptote
Zero, secant
Amplitude in a sine and cosine graph
“A” (first value)
Amplitude in secant, cosecant, and tangent
No amplitude
Formula used to find the period in a tangent graph
Pi/b
Angle
Two rays with the same initial point
Angles that measure between 0 and pi/2 (90) are
Acute
Shared initial point of two rays
Vertex of the angle
Angles that measure between pi/2 (90) and pi (180) are
Obtuse
Two positive angles are said to be _______ if the sum of their angles is pi/2 (90)
Complimentary
Two positive angles are said to be _________ if the sum of their measures is pi (180)
Supplementary
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
Two angles in standard position that have the same terminal side are said to be _____
Coterminal
To convert degrees to radians multiple degrees by
Piradians/180
To convert radians to degrees multiply radians by
180/piradians
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
The radian measure of any central angle is
The length of the intercepted arc divided by the circle’s radius
How to find a co-terminal angle
Add or subtract 360 degrees of 2pi
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
Sine=
Y and opposite/hypotenuse
Cosine=
X and adjacent/hypotenuse
Tangent=
Y/x and opposite/adjacent
cosecant=
1/y, hypotenuse/adjacent, 1/sin
Secant=
1/x, hypotenuse/adjacent, 1/cos
cotangent
X/y, adjacent/opposite, 1/tan
On the Unit circle for every 30 degrees you go ___ radians
Pi/6
On the Unit circle for every 45 degrees you go every ____ radians
Pi/4
Y=sin^-1x
[-pi/2, pi/2] (Q1 and Q4)
Y=cos^-1x
[O, pi] (Q1 and Q2)
Y= tan^-1x
(-pi/2, pi/2) (Q1 and Q4)
Pythagorean Theorem
A^2+B^2=c^2
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)
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)
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
component form
Magnitude of PQ
IIPQII= √(x2-x1)^2+(y2-y1)^2
Law of Sines
SinB/b=SinA/a
When do you use law of sines
ASA AAS
Law of consines
a^2=b^2+c^2-2(b)(c)(cosA)
When do you use law of cosines
SAS SSS
Note
Flashcard