How to break into a math book

In this seemingly unsolvable game of four people and four ghosts crossing the river, there is a bug, which is Tuhua.

According to the rules provided by the blacks, if the number of blacks on either side is greater than the number of challengers, the challengers will be killed by the blacks.But Tu Hua is an exception. He has a ghost stone and is the fiancé of the chief's daughter recognized by the tribe. This identity is his gold medal for avoiding death.

Tu Hua had never thought that this ugly and scumbag broken stone was so cute. He tossed the ghost stone back and forth with both hands, and leaned next to the black man and said, "If I die, your poor chief's daughter will be so cute." Don't you have no husband?"

The black man gritted his teeth and said, "...Yes."

Tu Hua smiled: "Then will you kill me?"

The black man continued to grit his teeth: "...No."

Tu Hua nodded contentedly: "Okay, then follow our arrangement and cross the canyon!"

According to their plan, eight rounds of back and forth can complete the task.First, Tu Hua and a black man crossed the canyon in a basket at the same time.Tu Hua took the lead in stepping up to help him sit firmly. Although the basket looked thin, it actually had a strong load-bearing capacity. A black man came and sat down with him, and it didn't appear to be wobbly.

The Negro took the helm and the basket slid swiftly into the fog.

After about a minute or two, the thick fog gradually faded, and what came into view was a completely different scene from the desert on the other side.There are lush jungles everywhere, the air is filled with the moisture of green grass, the trees are flourishing, and occasionally birds and squirrels will pass by.

After the basket stopped on the shore, Tu Hua let the black man go ashore and drove the basket back by himself.At this time, there were three black men and three challengers on the other side of the desert, and one black man on the other side of the rainforest, and Tu Hua was ferrying in a basket.

After arriving at the shore, Tu Hua took another black man there, and then went to the rainforest bank by himself, and let the black man ferry back again.That is to say, after the black man arrived, the game of four people and four ghosts had been transformed into a game of three people and three ghosts. There were three black men and three challengers on the desert bank, and one black man and one painted man on the rainforest bank.

Then, the third round.Tang Bo and a black man went to the basket. At this time, there were only two black men and two challengers left on the desert shore, and the number was even.After arriving at the rainforest bank, the black man went ashore, and Tang Bo ferryed back.After Tang Bo came ashore, there were two blacks and three challengers left on the desert bank, and two blacks and one painted on the rainforest bank.

Although the number of black people on Tu Hua's side was greater than the number of challengers, but because Tu Hua had a body protected by ghost stones, the black people did not attack him.

fourth round.This time, there were two black people in the basket, which meant that there were only Tang Bo, Sun Wei, and Wang Boyu left on the other side of the desert. After reaching the other side, one of the black people went ashore and the other ferryed back.At this time, there is one black man and three challengers on the desert bank, and three black men and one Tu Hua on the rainforest bank.Paint is still safe.

Fifth round.Sun Wei and Wang Boyu went to the basket, leaving only Tang Bo and a black man on the desert bank.After arriving at the shore, Sun Wei exchanged places with a black man, that is to say, Sun Wei went ashore, and the black man and Wang Boyu ferryed back together.At this time, there is a black man and Tang Bo in the desert bank, Wang Boyu and a black man in the basket, and there are two black men, Tu Hua and Sun Wei in the rain forest bank, the number is even.

Sixth round.The black went ashore, and Wang Boyu took Tang Bo into the cradle.At this time, there are two blacks on the desert bank, two challengers in the basket, and two blacks and two challengers on the opposite bank.After arriving at the shore, Tang Bo and Wang Boyu went ashore and let a black man ferry back.

In other words, the four challengers had safely reached the rainforest bank at this time, there was one black man on the rainforest bank, and three black men on the other bank.

The next two rounds are the business of the three blacks themselves, and they only need to ferry two more rounds before they can all go ashore.

So far, the game of four people and four ghosts crossing the river has successfully ended.

Sun Wei looked deep into the rainforest, lost in thought, and she acted as if she didn't hear Tu Hua talking to her.After a while, Sun Wei asked the leading black man, "Are we going northeast?"

The black man gave him a complicated look, and replied, "Yes."

Sun Wei's expression brightened instantly.She turned back to Tu Hua and the three of them and said excitedly: "I know what function it is!"

"Do you still remember the tips that the calculator gave us?" Sun Wei explained, "[Passing through deserts and polar regions, the function is in the rainforest. It is hot to the north and humid to the east.] We have experienced deserts, polar regions, and rainforests. After all, 'the function is in the rainforest' means that ... the function we're looking for is in the rainforest we're in right now."

"The next thing is the sentence [hot to the north, humid to the east]. It is this sentence that gave me the basis for judging the type of function." Sun Wei asked them, "Do you still remember the direction of our walking route?"

Tang Bodao: "We were in the cold polar region at the beginning. After we decided to go north, we arrived at the desert, which was very hot."

Sun Wei: "Yes, this is [Hot to the North]."

Wang Boyu said: "Then we met these four black people and followed them eastward to this tropical rainforest with plenty of rain."

Sun Wei continued: "Yes, this is [Damp to the East]."

Wang Boyu scratched his head: "But what conclusion can we draw from this?"

"Cartesian coordinate system." Tu Hua instantly understood Sun Wei's meaning, squatted on the ground and drew a Cartesian coordinate system with a tree branch, and gestured, "[The north is hot, the east is humid] This sentence is actually telling us, Temperature and humidity are the y-axis and x-axis that divide this Cartesian coordinate system."

Tu Hua's finger slides from the third quadrant of the coordinate system to the second quadrant: "We walk from the poles to the desert, and the temperature rises precisely because we are moving along the y-axis pointing north; while we are walking east , to the present rainforest, it is because we are moving along the x-axis pointing east."

In the blank space of the first quadrant, Tu Hua wrote the word "damp heat", the second quadrant "dry heat", the third quadrant "dry cold", and the fourth quadrant "damp cold": "That is to say , the place we walked is actually a huge Cartesian coordinate system divided by dryness, humidity and temperature."

"We have gone through three quadrants, only the fourth quadrant has not been there. If you guessed correctly, the fourth quadrant should be a world covered in ice and snow."

Sun Wei nodded and agreed with Tu Hua's explanation: "Then there is the function image in this coordinate system."

"I guess, the image of the function is the route of black people." Sun Wei picked up a branch and drew an arc in the second quadrant of the coordinate system, "First of all, I have observed the route of black people in the desert before, and they are indeed They came from the west, but to be precise, they came from the northwest."

"At the beginning, their footprints were infinitely close to the river we crossed, and then they moved further and further north, and their performance in the coordinate system was higher and higher, but this process was very slow and not very obvious." Sun Weidao , "In terms of mathematics, the function that takes their traveling route as an image is monotonically increasing in the second quadrant, and the increase is slow."

"Then we came to the first quadrant." Sun Wei drew another arc in the first quadrant with a branch, connecting with the arc in the second quadrant. Not northeast, he gave me a confirmed answer. That is to say, the graph of this function is also monotonically increasing in the first quadrant.”

A complete function graph is formed.This function increases monotonically over the entire domain of R, and only passes through the first quadrant and the second quadrant, and the value domain only contains all real numbers greater than 0.It increases slowly in the second quadrant, but rises sharply in the first quadrant. It is an upward arc.

Wang Boyu stared at the image, his eyes widened: "This is...an exponential function!"

The author has something to say: The saved manuscript is gone, and I won’t be home until tomorrow night. I guess I won’t be able to update it on time tomorrow. I will try to update it before midnight!