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42 Cards in this Set

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Names/meanings for: X
Domain, Independent Variable, Time, Input
Women have X chromosomes
Names/meanings for: Y
Range, Dependent Variable, Output
Men have Y chromosomes
Functions
Can't have repeating X values
Vertical line test (vertical line can only cross function once)
Corrdinate values
(X,Y)
X comes before Y in the alphabet
Axis labels
X axis-horizontal axis
Y axis-vertical axis
X goes left to right
Y goes up and down
Slope/Rate of Change
Change in Y's/change in X's
Vertical change/Horizontal change
(Y2-Y1)/(X2-X1)
Leans to right/goes up-Positive;
Leans to left/goes down-Negative;
Straight up and down-No slope;
Goes left to right-zero slope
Linear Function
y=mx+b;
m is slope;
b is y-intercept;
graph is a straight line
Line is first four letters of Linear
Quadratic Function
y=ax²+bx+c;
+a=U shaped;
-a=n shaped;
a=big whole #-U gets more narrow;
a=small fraction #-U gets wider
U in qUadratic describes the shape of the graph
Absolute Value
y=|x|;
any # for x - or + comes out positive;
ex: y=|-4| =4
V in Value describes the shape of the graph
Y Intercept
Where the function crosses the y-axis.
(0,#);
x is always 0
called "b" in slope intercept form
X Intercept
Where the function crosses the x-axis.
(#,0);
y is always 0
Also known as roots or solutions
Greater than or Equal to:
denoted by a solid point & arrow going right on # line
--or--
denoted by a solid line & shading above the line on a graph
left side is bigger than or = to the right side
Percents
Part/Whole= %/100
move decimal 2 places to the left
>
Greater than:
denoted by an open circle & arrow going right on # line
--or--
denoted by dotted line and shading above line on graph
left side has to be bigger than the right side
<
Less than:
denoted by an open circle & arrow goin left on # line
--or--
denoted by dotted line and shading below line on graph
Left side has to be smaller than the right side
Less than or Equal to:
denoted by solid point & arrow going left on # line
--or--
denoted by solid line and shading below line on graph
Left side has to be smaller than or = to the right
X^a * X^b
X^a+b
When you x your letters
you + your exponents.
(X^a)/(X^b)
X^(a-b)
When you / your letters
you - your exponents.
(X^a)^b
X^(a*b)
When you ^ a power to another power
you x your exponents.
a less than b
b-a
Less than=taken away from;
you have to have b before you can take a away from it
Associative property
(a+b)+c=a+(b+c)
(a*b)*c=a*(b*c)
You can associate with people around you without moving.
Commutative property
a+b=b+a
a*b=b*a
You commute to and from school.
Distributive property
a(b+c)=a*b+a*c
You have to distribute the a to everything in the parenthesis.
"Share the Love"
When you are given a table with info. & you have functions as answer choices
(Also works when given any two points or coordinates.)
1. Put table in STAT function & calculate either linear regression or quadratic regression
2. Put each function in y= and push 2nd Table and compare. (Equations must be in y=format)
STAT-EDIT-put x's under L1 & y's under L2-STAT-→-CALC-4 Linear Regress. or 5 Quadratic Regress.
a²+b²=c²
Pythagorean Thereom;
Can be used anytime you have a right △ and are missing only one side;
(Area of □ with side length a + Area of □ with side length b=Area of □ with side length c)
c=hypotenuse (always the longest side);
a+b>c;
a<c & b<c
Prefixes implying numerical values
mono-1;
bi-2;
tri-3;
quad-4;
penta-5;
hexa-6;
hepta-7;
octa-8;
nona-9;
deca-10
Parent Function
Linear y=x;
Quadratic y=x²;
Absolute Value y=|x|;
Square Root y=√x
The most basic forms of the function. Has no additional numbers to change the shapes and directions. It is your "starting point" for each type of function.
Point of Intersection
(x,y) where the x and y value solve each equation. They both make each equation true when the are plugged in and the equations are solved.
Where two lines touch.
Put each equation in Y=--
Graph--2nd--Trace--5 Intersect--Enter--Enter--Enter
Volume of a Cube
V=s³
V=l*w*h, but since all the side are the same for a cube then it is
V=s*s*s
Parallel Lines
The slopes are equal.
Ex:y=2x+5 and y=2x-7;
The slope is m=2 for both equations.
Both lines are leaning in the same direction.
# of Solutions: None
Two lines that never touch.
Ex: railroad tracks
Perpendicular Lines
Two lines that intersect at one point so that they form 90 degree angles where they cross. Looking like this: +;
The slopes are negative reciprocals of each other.
Ex: y=2/3x+5 & y=-3/2x+5;
The slopes are m=2/3 & m=-3/2
# of Solutions: 1
Take the first slope, flip it, and make it negative.
They form a "cross" when they intersect.
Identical Lines
Two lines that look the same.
Ex: y=3x-4 & y=3x-4;
These lines touch everywhere.
# of Solutions: infinitely many
When they are graphed you can only see one of them because they are on top of each other.
Scale Factor
Where you are going/
Where you are coming from

A # in fraction form comparing the same sides of 2 similar shapes expressing the amount of dilation that occured.
How much a shape shrinks or blows up.
If it shrinks, the small # is on top. ex: 1/2, 2/7, 3/8;
If it blows up, the big # is on top. ex: 2/1, 7/2, 8/3
Transformation
Sliding a shape on the coordinate grid or graph.
Translate=slide
(up ▲, down ▼, left ◀, or right ▶)
Rotation
Rotate a shape on the coordinate grid or graph.
To turn clockwise or couterclockwise. Spin
Dilation
Dilate a shape from it's original size.
* the coordinates by a scale factor.
Ex: Δ with points (1,1),(4,6),(8,-8);
Dilation by scale factor of 2:
2*{(1,1),(4,6),(8,-8)}=
{(2,2),((8,12),(16,-16)};
Dilation by a scale factor of 1/2:
(1/2)*{(1,1),(4,6),(8,-8)}=
{(1/2,1/2),(2,3),(4,-4)}
Reduce or enlarge a shape by a given scale factor.
Reflection
Reflect a shape on a coordinate grid or graph across a given axis.
The points must cross the axis of reflection no matter which side of the axis it is on.
Flip across the y-axis=like turn the page of a book.
Flip across the x-axis=like fliping over the page of a roladex.(upside down or right side up)
Surface Area of a Prism
Find the Area of all the surfaces in the prism and add them up.
Rectangular prism:
contains 6 ∓'s
2 (left & right sides)+
2 (front & back sides)+
2 (top & bottom sides);
Triangular prism:
contains 2 ∆'s & 3 ∓'s
Prisms have two eqaul bases. The shape of those bases determine the name of the prism. The lateral faces are all made up of rectangles.
Rectangular Prism=2 ∓ bases;
Triangular Prism=2 ∆ bases;
Cylindrical Prism=2 o bases
Multiplying Polynomials
When multipying polynomials: the # of terms in the 1st polynomial times the # of terms in the 2nd polynomial will give you the # of terms in your answer.
Ex: (2x+3)(5x-1)=10x²-2x+15x-3;
*This helps you not to forget a step.
Remember to distribute and then collect like terms.
(Always keep negatives with the # that it's in front of)
(1 term)(1 term)=1 term;
(1 term)(2 terms)=2 terms;
(1 term)(3 terms)=3 terms;
(2 terms)(2 terms)=4 terms;
(2 terms)(3 terms)=6 terms;
etc.
Exponents
x² is the same as x²/1;
x^-2 is the same as 1/(x²);
or
1/(x^-2)is the same as x²;
The negative exponent means that term must be moved to the opposite side of the fraction.
Negative exponent on top means it goes on the bottom.
Negative exponent on the bottom means it goes on the top.
Measuring using centimeters:
There are 3 different sized lines.
The longest lines are the whole # centimeter marks.
The middle length lines are the 1/2 centimeter marks.
The shortest lines are the 1/10 centimeter marks.
The # of the same sized lines in between each whole centimeter is the # of piece each centimeter is cut into.
Ex: 1/10 centimeters=there are 10 little lines in between each whole centimeter.
Measuring using inches:
There are 4 different sized marks.
The longest lines are the whole # inch marks.
The 2nd longest lines are the 1/2 inch marks (in the middle, between each inch).
The 3rd longest lines are the 1/4 inch marks.
The shortest lines are the 1/8 inch marks.
The # of same sized lines in between each inch are the # of pieces each inch is cut into.
Ex: 1/4 inch=there are 4 lines cutting each inch into 4 equal pieces.