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42 Cards in this Set
- Front
- Back
- 3rd side (hint)
Names/meanings for: X
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Domain, Independent Variable, Time, Input
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Women have X chromosomes
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Names/meanings for: Y
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Range, Dependent Variable, Output
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Men have Y chromosomes
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Functions
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Can't have repeating X values
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Vertical line test (vertical line can only cross function once)
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Corrdinate values
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(X,Y)
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X comes before Y in the alphabet
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Axis labels
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X axis-horizontal axis
Y axis-vertical axis |
X goes left to right
Y goes up and down |
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Slope/Rate of Change
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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 |
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Linear Function
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y=mx+b;
m is slope; b is y-intercept; graph is a straight line |
Line is first four letters of Linear
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Quadratic Function
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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
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Absolute Value
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y=|x|;
any # for x - or + comes out positive; ex: y=|-4| =4 |
V in Value describes the shape of the graph
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Y Intercept
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Where the function crosses the y-axis.
(0,#); x is always 0 |
called "b" in slope intercept form
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X Intercept
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Where the function crosses the x-axis.
(#,0); y is always 0 |
Also known as roots or solutions
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≥
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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
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Percents
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Part/Whole= %/100
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move decimal 2 places to the left
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>
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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
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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
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≤
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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
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X^a * X^b
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X^a+b
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When you x your letters
you + your exponents. |
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(X^a)/(X^b)
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X^(a-b)
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When you / your letters
you - your exponents. |
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(X^a)^b
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X^(a*b)
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When you ^ a power to another power
you x your exponents. |
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a less than b
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b-a
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Less than=taken away from;
you have to have b before you can take a away from it |
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Associative property
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(a+b)+c=a+(b+c)
(a*b)*c=a*(b*c) |
You can associate with people around you without moving.
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Commutative property
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a+b=b+a
a*b=b*a |
You commute to and from school.
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Distributive property
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a(b+c)=a*b+a*c
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You have to distribute the a to everything in the parenthesis.
"Share the Love" |
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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.
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a²+b²=c²
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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 |
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Prefixes implying numerical values
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mono-1;
bi-2; tri-3; quad-4; penta-5; hexa-6; hepta-7; octa-8; nona-9; deca-10 |
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Parent Function
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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.
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Point of Intersection
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(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.
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Where two lines touch.
Put each equation in Y=-- Graph--2nd--Trace--5 Intersect--Enter--Enter--Enter |
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Volume of a Cube
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V=s³
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V=l*w*h, but since all the side are the same for a cube then it is
V=s*s*s |
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Parallel Lines
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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 |
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Perpendicular Lines
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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. |
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Identical Lines
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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.
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Scale Factor
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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 |
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Transformation
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Sliding a shape on the coordinate grid or graph.
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Translate=slide
(up ▲, down ▼, left ◀, or right ▶) |
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Rotation
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Rotate a shape on the coordinate grid or graph.
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To turn clockwise or couterclockwise. Spin
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Dilation
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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.
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Reflection
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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) |
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Surface Area of a Prism
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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 |
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Multiplying Polynomials
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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. |
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Exponents
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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. |
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Measuring using centimeters:
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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. |
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Measuring using inches:
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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. |