Equivalent expressions/Equality in functions:
This just means that two expressions are the same
2(x-2) = 2x-4

Localization points is what these two intercepts are:

Y-intercept: When the x-value is 0 f(0), and the b-value of the function

X-intercept: When the y-value is 0 f(x) = 0

Second Order Functions: Functions that aren’t linear

Chronic functions/equations: Very advanced math

Origin in coordinate plane is the point (0, 0)

A x-value only has ONE y-value, but a y-value can have MULTIPLE x-values

The way to find a crossing point by just equaling the two equations and then you can find x and y coordinates

Solution of equation:
The number that will be put instead of the x, y, z, etc. that will then make the equation equal
2x = 4
X = 2
Because 2*(2) = 4

Stochastic function: A cloud of points, not a line
Input has one value, and outputs have multiple points

Symbolic representation: Representation of a function that we already know
AKA not stuff like integrals and other more complex functions

F(x): Means a function, NOT y, y is used for a numerical expression of a function’s value
The number in the (x) is the number that is replaced with “x” in the function
F(2) = f(x = 2)

Domain: Every possible x-value

Domain can be described as D: (-∞, 4) U (4, ∞) in a function where x can’t be 4, or you can write D: {x | x ≠ 4}

Range: Every possible y-value

Projection: This is the scribbly lines used for finding a point AKA an x and a y value

[ ]’s mean that the number is included in the interval, and ( )’s means that it is not included in the interval and is also used for -∞ and ∞
For, the domain is [2, ∞) AKA x ≥ 2

Unions (U): is just a way to separate intervals
For , domain= (-∞, -2) U (-2 , ∞) AKA every number, except -2

X = k is not a function, because one x-value has an infinite amount of y-value

When a function is just some data points AKA doesn’t really represent a linear, quadratic, etc. function but is still technically a function its domain and range are just those specific data points’ x and y-values
Domain: (-5, -4, -2, -1) NOT (-5, -1)
Range: (1, 3, 4, 5) NOT (1, 5)
They should still be in order from smallest to biggest though

Horizontal function: y=k
Has ONE y-value and infinite x-values
A horizontal line that goes through (5, -3), would be y = 3

Vertical function: x=k
Has ONE x-value and infinite y-values
A vertical line that goes through (5, -3), would be x = 5

Rules about shape equations:
If you for an example need to find the height of a box, then the height can obviously not be 0 or a negative number

Linear Factor:
(x-k), AKA the thing you get when factoring

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