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What is f 0. What does the notation y = f (x) mean in mathematics - Hypermarket of knowledge. Small aperture is really bad

25.12.2021

If you look at all the bags of seeds hanging or spread out on the counter, you can often see the designation "F1" indicated somewhere in the corner. This marking is quite common and can be seen on all types of vegetable crops. So what does F1 mean on seed? What features and characteristics are embedded in this designation? Let's try to figure out this abbreviation.

A little about breeding or what F1 means on seeds

With the beginning of the gardening period, or, more simply, with the onset of spring, all summer residents think about the issue of planting crops - what will be planted, where to plant it and in what sequence. But in any case, a vegetable garden begins with seeds - whether it is seeds independently harvested from grown crops, or purchased in a store, on the market.

Buying seeds is not an easy task, because you need not only to choose the same variety from the variety presented, but also to pay attention to the characteristics of the culture. And seeds marked F1 are also usually expensive. What is their quality? And can you then collect your own seeds from them?

What are F1 varieties and how do they differ from regular seeds

In general, the formula F1 denotes hybrid seeds. It comes from the Italian filli, which means "children", and the one appears as a symbol of the first generation. That is, hybrids are varieties obtained from the crossing of two other common varieties of a crop, which are the parents for the variety with the F1 designation.

Common varietal seeds are obtained through a long selection process, and carry constant characteristics such as yield, fruit color and size, vegetable taste, resistance to diseases, pests, weather conditions, etc. Over time, these characteristics of these varieties do not change. That is, seeds from crops grown from ordinary varietal seed will give exactly the same fruits as their parents.

This is not the case with hybrid seeds. They inherit the best qualities from their parents, give themselves completely - they grow quickly and give 100% abundant and beautiful harvest (with proper agricultural technology). But, unfortunately, their signs are not transmitted, so to speak, "by inheritance." Vegetables grown from F1 seed cannot produce the exact same crops with the same excellent traits.

What are the positive characteristics of hybrid seeds?

The breeding of hybrid seeds is not accidental. When crossed, they take on the best characteristics of the parents that the latter possess. That is, hybrid seeds take the dominant, pronounced, characteristics of the parents for themselves, and this is what breeders are guided by when breeding a hybrid.

Therefore, as a rule, F1 seeds have increased productivity, resistance to negative weather conditions, successfully resist diseases and pests, the fruits are large and even, and are characterized by accelerated growth. As a result, they have the hardiness that ordinary varietal seeds do not have. That is why hybrid seeds (assuming that they are real hybrid seeds, of course) germinate even when others do not, and give a good harvest in those years that are considered to be low-yielding. In addition, hybrids are most often self-pollinated, and this is a definite plus.

Of course, given these indicators, it is natural that the cost of seeds with the designation F1 differs from conventional varieties - they are more expensive. And much more time and effort is spent on obtaining them. By purchasing a real hybrid, you can be sure that it will give a good harvest (sometimes even in bad weather conditions) just in time, and maybe even earlier, and its fruits will be large, smooth and fleshy.

How F1 Hybrids Are Made

Hybrid seeds are obtained by crossing varietal seeds. This process is long, moreover, it is done manually, which partly explains the increased cost of the final planting material.

Since F1 seeds obtained by crossing take their dominant characters from their parents, they are careful about the selection of crossed varieties. For example, take one variety with increased characteristics of disease resistance, and the second variety is abundantly productive. As a result, the grower gets a hybrid that will give a good and healthy mega-harvest, and not a single vegetable bush will be bent from garden diseases.

Or, for example, the first variety will have the main feature of early maturity, and the second - the large size of the fruits, as a result, a large harvest will be obtained quickly, even before the ripening period of ordinary varieties. Or one parent will give resistance to bad weather, and the second - early maturity. And such traits for each specific species - the sea, and they are transmitted to F1 seeds in almost one hundred percent expression. Although in some cases, "children" are superior to "parents" by 20 percent. Getting a unique hybrid is kept secret by the producers - from which varieties it was bred.

But getting such seeds is troublesome. Firstly, those varieties from which they prefer to obtain a hybrid are grown in greenhouses. But parents should not only have pronounced dominant characters, they should be of the same species, and also be self-pollinating. On one of the plants, at the moment it begins to bloom, the stamens are forcibly removed. And pollen is collected from a plant of another variety, which, of course, happens with the help of special equipment. The first plant is treated with the obtained pollen. This process takes several months, every day, resulting in hybrid seeds.

Disadvantages of F1 seeds

We found out about the excellent qualities and positive aspects of using F1 seeds when growing a crop. But all the pleasures in life come at a price. So what is negative when using these seeds?

First, as we said, is the cost. The price for hybrid seeds exceeds (and sometimes several times) the prices of conventional varietal seeds.
Secondly, it is impossible to grow a crop for the next year from F1 seeds. As mentioned above, the second generation of hybrid seeds does not inherit the traits of the parents - neither yield, nor early maturity, nor size qualities of fruits, nor resistance to diseases and weather. In other words, there is no need to harvest seeds from vegetables obtained from F1 planting material - this is from the category of "monkey labor". These second-generation harvested seeds may not give what you expect, and an incomprehensible variety of non-fertile crops will grow from them. Or fruiting, but not with the expected quality.
Thirdly, if we turn to the biochemical composition of varietal plants and plants grown from F1 seeds, then it is different. Adherents of everything natural suggest that the first group is closer to wild plants, which means that it is the usual breeding varieties that give vegetables rich in trace elements and vitamins, while hybrids do not have so many of them at all. Nonsense, of course - their amino acid composition is normal, but whether the plant has accumulated a sufficient amount of sugars depends on the growing conditions. It is unlikely that a vegetable intended for indoor cultivation will pick up the "due" glucose in the garden bed. Therefore, we will highlight this item separately.
Fourth, agricultural technology. Still, no matter what super-properties the hybrid has, it reveals all its excellent characteristics only with proper care. Otherwise, he does not always show them.
Well, and fifthly, taste. Unfortunately, hybrids do not get all the variety and nuances of taste from their parents. Sometimes they are significantly inferior to varietal crops in terms of taste, but this is not always the case. Why is it believed that hybrid crops have more oak flavor? Perhaps this impression was fixed from the purchase of winter greenhouse vegetables. But after all, it is understandable - with a lack of light, photosynthesis is less pronounced, and less glucose is produced.

You can take strawberries as an example - it is clear that wild strawberries are tastier and more aromatic than they are from the garden, and large store strawberries (especially in winter), which have only a small fraction of real taste, cannot be compared with them.

But we, for example, know the finest sweet tomatoes from the F1 series - Red Date, Yellow Date and Orange Date. Our grandchildren love to eat them right from the garden. But in the last rainy summer, they did not pick up the sweetness - the taste was almost neutral.

Another thing is that when choosing certain qualities in hybridization, an unsuccessful combination can really turn out. For example, the genes for the perfect round shape and the genes for the red color, when combined, can produce absolutely beautiful fruit without taste. Or in pursuit of a hybrid resistant to late blight, we get a sour hybrid.

That is why we prefer to choose crooked-oblique-yellow-green-orange-black-variegated tomatoes. First, there must be variety in the beds. Secondly, if the weather fails, then the taste of your favorite variety can be replaced by an understudy. And sometimes you want to try new ones. But over time, the list of preferences has settled down, there is always a gentleman's set of "favorites" for planting.

The nuances of growing bunch cucumbers

I would like to add about the fact that the taste of hybrids may not live up to expectations, not only because of crossing, but also because of flaws in agricultural technology. This is especially evident in the hybrids of cucumbers, which give a bundle ovary (10-15 zelents are formed in the axils). Almost all of our friends bought such F1 varieties and were disappointed - none of them had a picture from the cover. Most likely, the scheme of plant formation was simply not taken into account. And the seed bag must have a drawing. Briefly, the meaning of the formation is as follows:

you need to preserve the central whip, and not transfer it to lateral shoots, as was customary when growing old varieties;
blind the lower 5-10 (depending on the variety) of the node - leave only the leaves, and remove the lateral branches and embryos of the greens altogether.

That is, the technique is the same as that of peppers, when we remove the first ovary - we "save" strength and nutrients for future abundant fruiting. The plant must develop a good root system and gain what is called an appropriate green mass, then the yield will be impressive.

And if you do not dazzle, then the plant reproduces as usual - in each node, one, well, at most two, cucumbers are formed. But they are early, you say. But you can plant cheaper planting material for the early ones, right? Why ruin an elite sludge?

We hope you figured out what the abbreviation F1 means on seeds, and you can safely select varieties for open and closed ground. Do not stop at one variety, grow a wide range of even one crop - this will save you from disappointment in a bad year and will have something to compare!

>> Mathematics: What does y = f (x) mean in mathematics

What does y = f (x) mean in mathematics

When studying any real process, they usually pay attention to two quantities participating in the process (in more complex processes, not two quantities are involved, but three, four, etc., but we are not yet considering such processes): one of them changes as if by itself, regardless of anything (we denoted such a variable by the letter x), and the other quantity takes on values that depend on the selected values of the variable x (we denoted such a dependent variable by the letter y). Mathematical model the real process is just the writing in mathematical language of the dependence of y on x, i.e. the relationship between the variables x and y. Let us remind once again that by now we have studied the following mathematical models: y = b, y = kx, y = kx + m, y = x 2.

Do these mathematical models have anything in common? There is! Their structure is the same: y = f (x).

This notation should be understood as follows: there is an expression f (x) with a variable x, with the help of which the values of the variable y are found.

It is no coincidence that mathematicians prefer the notation y = f (x). Let, for example, f (x) = x 2, that is, we are talking about function y = x 2... Suppose we need to select several values of the argument and the corresponding values of the function. So far we have written like this:

if x = 1, then y = I 2 = 1;
if x = - 3, then y = (- 3) 2 = 9, etc.

If we use the notation f (x) = x 2, then the record becomes more economical:

f (1) = 1 2 = 1;
f (-3) = (-3) 2 = 9.

So, we got acquainted with one more fragment mathematical language: the phrase "the value of the function y = x 2 at the point x = 2 is equal to 4" is written shorter:

"If y = f (x), where f (x) = x 2, then f (2) = 4".

And here is a sample reverse translation:

If y = f (x), where f (x) = x 2, then f (- 3) = 9. In another way, the value of the function y = x 2 at the point x = - 3 is 9.

EXAMPLE 1. Given a function y = f (x), where f (x) = x 3. Calculate:

a) f (1); b) f (- 4); c) f (o); d) f (2a);
e) f (a-1); f) f (3x); g) f (-x).

Solution. In all cases, the plan of action is the same: you need to substitute in the expression f (x) the value of the argument that is indicated in parentheses instead of x, and perform the appropriate calculations and transformations. We have:

Comment. Of course, instead of the letter f, you can use any other letter (mainly from the Latin alphabet): g (x), h (x), s (x), etc.

Example 2. Two functions are given: y = f (x), where f (x) = x 2, and y = g (x), where g (x) = x 3. Prove that:

a) f (-x) = f (x); b) g (-x) = -g (x).

Solution. A) Since f (x) = x 2, then f (- x) = (- x) 2 = x 2. So, f (x) = x 2, f (- x) = x 2, so f (- x) = f (x)

b) Since g (x) = x 3, then g (- x) = -x 3, i.e. g (-x) = -g (x).

The use of a mathematical model of the form y = f (x) turns out to be convenient in many cases, in particular, when the real process is described by different formulas at different intervals of variation of the independent variable.

Let us describe some properties of the function y - f (x) with the help of the graph plotted in Figure 68 - such a description of the properties is usually called reading the graph.

Reading a graph is a kind of transition from a geometric model (from a graphical model) to a verbal model (to describing the properties of a function). A
plotting is a transition from an analytical model (it is presented in the condition of example 4) to a geometric model.

So, we proceed to reading the graph of the function y = f (x) (see Fig. 68).

1. The independent variable x ranges over all values from - 4 to 4. In other words, for each value of x from the segment [- 4, 4], you can calculate the value of the function f (x). They say this: [-4, 4] - the domain of the function.

Why, when solving Example 4, did we say that f (5) cannot be found? Because the value x = 5 does not belong to the scope of the function.

2. y naim = -2 (the function reaches this value at x = -4); At the nanb. = 2 (the function reaches this value at any point of the half-interval (0, 4].

3.y = 0 if 1 = -2 and if x = 0; at these points the graph of the function y = f (x) intersects the x-axis.

4.y> 0, if x є (-2, 0) or if x є (0, 4]; on these intervals, the graph of the function y = f (x) is located above the x-axis.

5.y< 0, если же [- 4, - 2); на этом промежутке график функции у = f(x) расположен ниже оси х.

6. The function increases on the segment [-4, -1], decreases on the segment [-1, 0] and is constant (neither increases nor decreases) on the half-interval (0.4].

As we explore the new properties of functions, the process of reading the graph will become richer, more meaningful and interesting.

Let's discuss one of these new properties. The graph of the function considered in example 4 consists of three branches (of three "pieces"). The first and second branches (a straight line segment y = x + 2 and a part of the parabola) are “docked” successfully: the segment ends at to point (-1; 1), and the parabola segment starts at the same point. But the second and third branches are less successfully “docked”: the third branch (a “piece” of the horizontal line) begins not at the point (0; 0), but at the point (0; 4). Mathematicians say: "the function y = f (x) undergoes a discontinuity at x = 0 (or at the point x = 0)." If the function has no discontinuity points, then it is called continuous. So, all the functions that we met in the previous sections (y = b, y = kx, y = kx + m, y = x2) are continuous.

Example 5... A function is given. It is required to build and read its schedule.

Solution. As you can see, here the function is defined by a rather complex expression. But mathematics is a single and integral science, its sections are closely related to each other. Let's take what we learned in Chapter 5 and shorten algebraic fraction

is valid only under the restriction.Consequently, we can reformulate the problem as follows: instead of the function y = x 2
we will consider the function y = x 2, where We construct a parabola y = x 2 on the coordinate plane xOy.
The straight line x = 2 intersects it at the point (2; 4). But by condition, it means that we must exclude the point (2; 4) of the parabola from consideration, for which we mark this point in the drawing with a light circle.

Thus, the graph of the function is built - it is a parabola y = x 2 with a "punctured" point (2; 4) (Fig. 69).

Let's move on to describing the properties of the function y = f (x), i.e., to reading its graph:

1. The independent variable x takes any values, except for x = 2. Hence, the domain of the function consists of two open rays (- 0 o, 2) and

2. y naim = 0 (attained at x = 0), y naib _ does not exist.

3. The function is not continuous, it undergoes a discontinuity at x = 2 (at the point x = 2).

4.y = 0 if x = 0.

5.y> 0 if x є (-oo, 0), if x є (0, 2) and if x є (B, + oo).
6. The function decreases on the ray (- ω, 0], increases on the half-interval.

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A. V. Pogorelov, Geometry for grades 7-11, Textbook for educational institutions

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Camera aperture - what is it anyway? And why is this value indicated after the number of pixels in the smartphone's photo matrix? Do not know? Let's figure it out, along the way figuring out which of the apertures is better.

What is aperture?

In simple terms, the aperture is the pupil. Light travels through the cornea (lens), passes through the pupil (aperture / diaphragm) and enters the optic nerve (photomatrix). Why is there an aperture in this chain? Yes, then, to dose the light radiation. The larger it is (the pupil dilates), the more light will enter the matrix (optic nerve).

F 2.0 aperture - what does it mean? Where is the aperture measured?

From the characteristics of smartphones, it is clear that the aperture is measured in special units - f-numbers. Or, as professional photographers say, in f-stops. Moreover, the size range of the aperture consists of fractional numbers - f / 1.4, f / 2.0, and so on. Sometimes a simplified designation is written in the characteristics - aperture 1.8. However, an accurate display of this value requires the following spelling - f / 1.8.

According to the laws of mathematics, the maximum value of the aperture is reached at the minimum value of the divisor - the numerical coefficient located on the right. That is, an aperture of 2.0 (f / 2.0) suggests a greater degree of pupil-aperture "expansion" than an aperture of 2.2 (f / 2.2). And the higher the number on the right, the lower the degree of aperture opening.

How does aperture size affect image quality?

A large aperture allows the lens shutters to open to the maximum, letting in a very large portion of light onto the sensor. A small aperture means that the lens curtains have not fully opened and allowed a minimum of light to enter the matrix.

How does this affect the image quality? Yes, in the most direct way! A large aperture in bright light is more likely to spoil (expose) the frame. Try taking a photo with the sun behind you and you will see all the consequences of too large an aperture. However, another situation is possible, when too small aperture value does not allow the matrix to capture a sufficient portion of light and the picture turns out to be dark.

That is, a good aperture can be neither large nor small. It should be suitable for the specific shooting conditions. However, in low light conditions, you need the largest aperture possible to capture the maximum light. And you shouldn't forget about it.

Is a small aperture really bad?

Not really. At small apertures - from f 4.0 - f 8.0 and below - there is an interesting opportunity to increase the depth of field of the matrix. The smaller the aperture, the more objects are in focus of the camera. Therefore, small aperture values are loved by all landscape photography fans and portraitists who want to get clear pictures without blurring outlines and other noise.

In the end, choosing between f 2.0 and f 2.2 which is impossible to say better. The first value guarantees the ability to improve the quality of the photo in a dark room. The second - promises to increase the sharpness of the picture.

Choosing a smartphone by the camera aperture

The trouble with any camera of any smartphone is the very small physical size of the photomatrix (the optic nerve of a mobile device). Therefore, the standard aperture of the main camera is f 2.0 or f 2.2. Not a single smartphone manufacturer that respects its customers will dare to set a lower aperture value. In this case, indoor photos will be completely unreadable.

A smartphone does not need too large an f-number either. It is easy to oversaturate the small sensor with light, ruining the balance of the picture. However, recently there have been devices with a dual camera and an aperture of f / 1.7, which is very good for a smartphone with an enlarged sensor. The quality of images indoors for such smartphones is at an unattainable height.