# data[].attributes.headline
Rinsing left, Falling right - y=-x^n when n is odd and greater than 0

# data[].attributes.subject
Rinsing left, Falling right - y=-x^n when n is odd and greater than 0

# data[].attributes.body
One significant characteristic of an odd function is that the ends of the graph behave as opposites of each other. In other words, when one end falls, the other end is guaranteed to rise. In the case of a negative leading coefficient,  the left side rises while the right side falls. An example would be the graph of y=-x^3 attached below.
Crazy Random Connection: the Isolationism In Ming and Qing dynasty
The Ming and Qing dynasty marked the end of Chinese feudal bureaucracy. The Song dynasty initiated strict restrictions on foreign trading (especially overseas) with harsh punishments, such as trades exceeding about 6 dollars* of worth was considered a crime, trades exceeding about 230 dollars* of worth could get you in jail for at least a year, and trades exceeding about 850 dollars* meant exiling to an isolated island with a permanent forced tattoo of shame on your face. It only got worse and worse later on, and eventually leads to lack of new ideas and information and deceleration of development of China as a whole. This piece of history would resemble the graph of y=-x^3 observed from left to right----never stopped getting more and more negative.

Remeber: the world "Isolationism" has "on(odd negative)" and therefore a negative odd polynomial function would help you to remember the history!

"But... but what's the point of remembering all these anyway?"

# data[].attributes.headline
Falling Left, Rising Right - y=x^n when n is odd and greater than 0

# data[].attributes.subject
Falling Left, Rising Right - y=x^n when n is odd and greater than 0

# data[].attributes.body
As mentioned in the previous post, when the ends of the graph behave differently, the function is an odd function. In the case of a positive leading coefficient, the left falls when the right rises. An example of a positive odd function would be the graph of y=x^3 attached below.
Crazy Random Connection: Communist China/Mainland
Communism was actually working China until 1966, marking the beginning of Cultural Revolution and corruption of the government system. The economy eventually stopped plummeting in 1978, when Deng Xiaoping, the President of Chinese Communist Party opened up China's economy to capitalism. This graph, from left to right, would look like a local max before a local min and eventually shoots up from the local min and hopefully extends to positive infinity.

Now, have fun trying to figure out a way to remember this absolutely interesting but weird and relatable connection!

I'm just lazy to figure another way out.

# data[].attributes.headline
Rising left, Rising right - y=x^n when n is even and greater than 0

# data[].attributes.subject
Rising left, Rising right - y=x^n when n is even and greater than 0

# data[].attributes.body
As mentioned in the previous post, when both ends of the graph behave the same way, in this case, both rising, the degree of the polynomial would be even. In the case of a positive leading coefficient, or the coefficient of the highest degree monomial of the polynomial function is positive, both ends of the graph rise. An example would be the graph of y=x^2 attached below.
Crazy Random Connection: the Qin, Sui, and Tang dynasties
The cruel and abusive reign son of Shi Huangdi, the first emperor of the Qin dynasty had only lasted seven years(210 BCE---207 BCE) before revolution and violence erupted. The Sui dynasty only lasted about 37 years before being overthrown again because the construction of the Great Canal had cost millions of lives. However, Tang Gaozu, the first emperor of the Tang dynasty, had reunited China, and his son, Tang Taizong was regarded as the most accomplished emperor in the Tang dynasty and even in the history of China by laying the foundation for the Golden Age that his successor had worked their butts off to achieve in this time period. If the graph is observed from left to right, you'll notice two local mins, one taking place at the end of the Qin dynasty and the other at the end of Sui dynasty with an extremely steep slope connecting the two.

How you're going to remember this? This is a good question... In the French alphabet, the "i" is pronounced as "e" in English, and there is one "i" in "Sui" and another in "Qin". So that should be good enough. For the even part, there are two "n"s, one in "Sui" and the other in "Tang". Two negative is also the same as a positive. There you go.

"But... but... this is too far-fetched..."

# data[].attributes.headline
Falling left, Falling right - y=-x^n when n is even and greater than 0

# data[].attributes.subject
Falling left, Falling right - y=-x^n when n is even and greater than 0

# data[].attributes.body
One significant characteristic of an even function is that both ends of the graph behave the same way. In other words, when one end falls, the other end is guaranteed to fall, too. In the case of a negative leading coefficient, which means the coefficient of the monomial with the highest degree of a polynomial function is negative, both ends of the graph fall. An example would be the graph of y=-x^2 attached below.
Crazy Random Connection: the Eastern Zhou period, the period of warfare, and the birth of many important philosophies such as Taoism, Confucianism, and Legalism
In this time period, China is broken into many independent states that never stopped conquering each other. The graph, if observed from left to right, can be compared with the growth of the six major states of the time that were eventually conquered by the Qin.
Let's pick the state of Wei as an example. The emperor that brought Wei to its absolute max was called King Wen of Wei. Unfortunately, the emperors after him weren't able to build upon the great work of King Wen of Wei that the state of Wei couldn't help but fall on the slippery slope to doom and eventually conquered by the state of Qin which led to the beginning of the Qin dynasty.

To remember all that historical connection stuff, think of "even" and "negative" abbreviate to "en"---there is an "en" in the name "King Wen of Wei", so you can remember this brilliant ruler by the "even degree polynomial" and "negative leading coefficient" end behavior!

"But... but... I thought this is a math class?"