Pre-Calc final

Function Notation

Function 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

PQ <x2-x1,y2-y1>

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