**Equivalent expressions/Equality in functions:**

This just means that two expressions are the same

Ex.

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

Ex.

**Solution of equation:**

The number that will be put instead of the x, y, z, etc. that will then make the equation equal

Ex.

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

Ex.

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

Ex.

**[ ]’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 ∞

Ex.

For, the domain is [2, ∞) AKA x ≥ 2

**Unions (U):** is just a way to separate intervals

Ex.

For , domain= (-∞, -) U (- U (, ∞)

**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**

Ex.**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

Ex.

A horizontal line that goes through (5, -3), would be **y = 3**

**Vertical function:** x=k

Has ONE x-value and infinite y-values

Ex.

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