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Vertical line test
tests if a relation is a function or not. If a vertical line intersects the relations graph in more than one place, then NOT a function

Function
a process for turning one number (like x) into another (like y). A rule that pairs a bunch of numbers in one set called a Domain into another set called a Range so that no x value repeats. the result is a set of ordered pairs (like x,y)

Domain / Input / Independent variable
the set of Independent Values or the x's

Range / Output / Dependent variable
output values from a function or relation or the y's

Increasing function
its graph rises from left to right. a function increases if f(a) > f(b) for every a > bin the interval.

Decreasing function
its graph decreased from left to right. a function decreases if f(a) > f(b) for every a < b

Maximum (turning point)
largest value of function on an interval

Minimum (turning point)
smallest value of a function on an interval

Vertex
point where function reaches a max or min, so either a Maximum or Minimum

Continuous graph / function
Function is continuous at a point (x,y) if it is defined at that point and passes through without a break. Can trace it without lifting pencil.

Discontinuous graph / function
Cannot be traced without lifting pencil.

Function notation
f(x) is "f of x" where x is the input value and the f(x) is the output value. apply the rule "f" to the number "x"

Set notation
to show the solutions to an equation. {(x,y)  y = 3x + 2} or "the set of ordered pairs x,y such that y = 3x + 2"

Value of a function
The value of f(x) at x or value of y. Find the value by "evaluating the function"

Evaluating a function
The independent value x is the "placeholder," so plugging in the xvalue and getting the y is evaluating the function.

Asymptotes
A graph never intersects a vertical asymptote but can intersect a horizontal asymptote. Think of a graph with 2 roots (crosses the xaxis) and then approaches the xaxis but never touches it

End behavior
Directions of the ends of a graph. Think of large x on a graph; then what is it doing at the far right or far left.

Multiple representations of functions
functions can be represented by graphs, tables, function notation like f(x), mapping diagrams, or words.

Translation / transformation of a function
An operation that shifts a graph horizontally, vertically or both. Think of y =mx + b and then add 2 to "b" and it shifts the line up by 2 points.

Parent Function
 A function with its simplest algebraic rule for its shape.
 This is when you love your Daddy.

Family of functions / types of function
Functions with common characteristics due to a common algebraic form or similar geometric shape. Think of a function that is shifted up by adding 2 or a parent punction and all its shifts up or sidways.



5kkkkkk  8kkkkkk =
3k to the 6th power

any number to zero power is =
1

12 to the negative 1 is =
1/2

define irrational number
any real number that cannot be expressed as a ratio a/b where a and b are integers with b nonzero

reciprocal
 interchange the numerator and the
 denominator i.e. invert the
 fraction

coefficient
 a number in front of a variable. For example in the
 expression x210x+25 the coefficient of the x2 is 1

absolute value
the numerical value of a real number without regard to its sign

associative property of multiplication
 when multiplying three or more real numbers the product is always the same regardless of their grouping
 (a × b) × c = a × (b × c)

area of a trapezoid
 =1/2 (b1+b2) h
 =h/2 (b1+b2)

difference of 5 and 8
13

area of rectangle with sides 12 and 5
60

Between what two integers is neg square root of 27
5 and 6 becasue square of 25 is 5 and 6 squared is 36

graph numbers on number line
7/2  1.8  square root of 6  neg sq root of 36  pi
6______3.5_______0__1.8___2.45___3.14

96 (1820)^{2}
9 6(2)^{2 }= 96(4) = 15

3x^{2}(4+8x) when x= 2
3(4)(12) = 24

simplify (y4x) + 6x  10y
 = y +4x +6x 10y
 = 11y + 10x

1/4 (x2) =8
 x/41/2 = 8
 x/4 = 8.5
 x/4 = 17/2
 x = 17*4/2 = 68/2 = 34

3(6x1) = 10x+11
 18x3=10x+11
 8x = 14
 x = 14/8 = 7/4

2x8 + 10 = 20
 2x16 +10 =20
 2x = 26
 x= 13

solve for y: 3x 9y = 15
 9y = 3x15
 y = 1/3(x) + 5/3

Solve for C: F = (9/5) C +32
 F  32 = (9/5) C
 (5/9)F  (5/9)32 = C

Solve for A: B = (3/5)(A+8)
 (5/3)B = (A+8)
 (5/3)B 8 = A


3/11  1/2 =
6/22  11/22 = 5/22

(2/3) / (8/5) =
(2/3)*(5/8) = 10/24 = 5/12

2/7 + 3/5 =
10/35 + 21/35 = 31/35


(2/7)  3 =
2/7  21/7 = 19/21

4/(7/9) =
(4/1) / (7/9) = (4*9)/7 = 36/7

(4/5) / 6 =
(4/5) / (6/1) = 4/30 = 2/15

8 / (C/3) =
(8/1) / (C/3) = 24 /C

4/a  pi/3 =
12/3a  4pi/3a = (124pi)/3a

a/b + c =
a/b + bc/b = (a+bc) / b

the slope of y = mx + b is
m

the yintercept of y=mx+b is
b

the slope of (A)X + (B)Y = C
A/B

the yIntercept of (A)X + (B)Y = C
C/B

To find the yintercept just substitute in _______ for the x coordinate
zero

