Patterns in Algebraic Functions
It is important to look for patterns in functions, between the x and y.
Linear: The 1st difference between x is constant, the 1 st difference between y is constant.
Quadratic: The 1st difference between x is constant, the 2
Lines
Lines are important and form the basis of linear algebra.
They can be applied in many real world uses as seen through roads, architecture, and bridges.
Lines are formed with the formula y = mx + b
This formula can have variations by changing the slo
Rational Function
In linear algebra, you may encounter lines with the formula of y = 1/x
These functions are not solely limited to one line, and can range to be 2+ lines.
They always display limits, such as x can not be equal to 0. Y can not be equal to 0
Linear Algebra: Cubic
Cubic functions are another type of line that can be tricky to people if they do not have the sufficient
information.
Cubic functions are represented by the formula ax^3 + bx^2 + cx + d
Since the first x has an odd exponent, 3, it is
Quadratic Lines
In linear algebra, you will also encounter parabolas in various scenarios.
Parabolas are expressed in the formula of ax^2 + bx + c.
These lines can either face upward or downward depending on whether the beginning is positive or
negative.
Linear Lines
In linear algebra, you should become familiar with the concept of lines.
Lines are expressed by the formula of y = mx+b
m is the slope
x is x
and b is the y-intercept
As noted in a previous document, the slope is calculated from rise over run
Lines
This lesson will teach you about the structure and different types of lines.
Any line with two arrow heads at the end is known as a line
Any line with only one arrow head at the end and a dot at the other end is known as a ray
Any line with two dots
Working the Quads
In this lesson we will be strengthening our quads (not the muscle, but the function).
Quadratic functions are easily identifiable from their familiar appearance of a parabola.
While quadratic functions are not a straight line as seen in
Is it a Function?
In linear algebra, you are given a variety of lines that may or may not be a function.
While they may appear normal, you must undergo several tests to figure out if it is a function.
1. Are there more than 1 y-values for 1 x-value?
Examp
Slopes
In linear algebra, you should be familiar with slopes. The slope is the rise/run within a line. Throughout
algebra, you will encounter different types of lines, and some of them may have no definitive slope.
However, by the end of the lesson, you c
Linear Algebra: Inverse functions
Similar to a reflection, lines can have inverses which are represented by f^-1 (x)
Inverse functions are reflected across the y = x line.
These functions show symmetry with each other and are identical lines. The only dif