Mod 4 sec 3

Function

a type of relation where each input (x) has exactly one output(y) aka each x has one y

Quad 1

+,+

Quad II

-,+

Quad III

-,-

Quad IV

+,-

Intercepts

where the function crosses the axis (either x or y)

Relative extrema

Refers to the max and min points on a function’s graph

Asymptotes

is like an invisible boundary line that a graph gets really close to but never touches

Upward vertical shif by k unitst

g(x) = f(x) + k (pos shift up)

Downwards vertical shift by k units

g (x) = f(x) - k (neg shift)

Shift to the left by k unit

g(x) = f(x + k)

Shift to the right by k unit

g(x) = f(x - k)

vertical stretch

(x) = kf(x)

Vertical compression, 0 < k < 1 (bigger than 0, smaller than 1)

g(x) =kf(x)

Horizontal stretch

g(x) = f (kx)

Horizontal compressions

g(x) = f (kx)

Reflection over the x axis

g(x) = -f(x), multiply entire function by-1

Reflection over the y axis

g(x) = f(−x), replace it with it’s -x

Angle

formed when two rays share an end point

Intersecting lines

lines that pass through the same point

Perpendicular lines

lines that intersect at right angles

Parallel lines

are lines that never intersect

A triangle has how many sides

3

A pentagon has how many sides

5

A hexagon has how many sides

6

A heptagon has how many sides

7

An octagon has how many sides

8

A nonagon has how many sides

9

A decagon has how many sides

10

A hendecagon has how many sides

11

A dodecagon has how many sides

12

An n has how many sides

n-gon

Point

an exact location in the space or a flat surface

Equilateral triangle

all sides and angles are congruent (the same)

Acute triangle

all angles are less than 90 degrees

Obtuse triangle

one angle is greater than 90 degrees

Right triangle

1 right angle and 2 acture angles

Isosceles triangle

2 sides are equal in length

Scalene triangle

no congruent (same) sides

Quadrilateral

a polygon w 4 sides and 4 vertices, sum of the interior angles is 360

Rectangle

A quadrilateral with opposite sides equal and four right angles

Square

A rectangle with four congruent sides and four right angles

Trapezoid

A quadrilateral with one set of parallel lines

Parrallelogram

a quadrilateral with opposite sides equal and two sets of parallel lines

Rhombus

A quadrilateral that is a parallelogram with all sides congruent

1 foot =

12 in

1 yard=

3 ft

1 mile=

5280ft

16 oz =

1lb

1 gallon =

4 quarts

1 kg =

2.2lbs

1in=

2.54 cm

1 millileter =

1 cubic cm

1 meter

3.28 ft

1 kilometer =

.62 miles

Angles

created when two rays intersect at a point, forming a vertex

Plane

a flat surface that only exists in two dimensions and extends infinitely in those dimensions, has length and width (like a piece of paper), but no height

Polygon

a figure on a plane that is closed, formed by three or more line segments where consecutive sides intersect at endpoints

Complimentary angles

two angles whose sum equals 90 degrees

Supplementary angles

two angles whose sum equals exactly 180 degrees

Two angles are adjacent

if they share a common vertex and side but no interior points

An angle bisector

is a ray that divides an angle into two angles that are congruent.

Perpendicular lines

intersect and create all right angles at the intersection

Kilo

1,000

Hecto

100

Deca (or Deka)

10

Base unit (meter, liter, gram)

1

Deci

1/10 (or 0.1)

Centi

1/100 (or 0.01)

Milli

1/1,000 (or 0.001)

Relation

any set of ordered paris

• Ex: (1,2), (8, 9)

• X value of 1, paired w a y value of 2

Linear functions

produce straight lines, subtype of polynomials in which the degree of the function is 1, have a constant rate of change

• Ex standard form: 6x - 3y = -9

  • Point slope form: y - 11 = 2 (x-4)

  • Slope intercept form: y = 2x +3

Quadratic functions

create a parabola, subtype of polynomial function, in which the degree of the function is 2.. f(x) aka y

• do not have a constant rate of change and increse/decrease by a multiple of its based

• Ex: standard form: f(x) = 2x^2 + 3x + 1

  • Vertex form: f(x) = (x + 0.75)^2 - 0.125

  • Intercept form: f(x) = (x + 1) (2x + 1)

Square root functions

are a subtype of radical function in which the input variable is underneath the sq root, inverse of a quadratic function

Polynomial functions

a function that contains real number coefficients and pos integer exponents (quadratic, cubic and quartic functions)

• Ex: x^3 + 2x^2 - 5x -6 or (x + 3) (x + 1) (x - 2)

Exponential function

has a constant proportional rate of change, input in the exponent

• The function keeps growing or shrinking at a steady rate, like doubling or halving over and over again

• Ex: f(x) = 2^x

Piecewise functions

a function described by the inclusion of multiple functions along different of its domain

Line

a collection of points that continues forever in both directions

• Ex: ←—-----> line keeps going on

Line segment

a part of a line with two end points

Ray

starts from one point and extends in one direction forever

• Ex: •—------>

A quadrilateral has how many sides

4

• Ex: square, rhombus, trapezoid, rectangle, parallelogram)

Iteration

When we measure something, we sometimes have to use the same tool over and over again to see how long or big something is.

• Ex: If your ruler is only 1 foot long, but your table is 6 feet long, you have to move the ruler 6 times to measure the whole thing!

Additivity

If we measure parts of something, we can add those parts together to find the total.

• Ex: If one piece of rope is 2 feet and another is 3 feet, you can add them to find the whole rope is 5 feet long.

Invariance

No matter what tool you use, the object you're measuring doesn’t change in size.

• Ex: A pencil is still the same length whether you measure it in inches, centimeters, or jellybean