Draw a graph to establish correspondence between the signs. GIA

y = khx + b. Establish a correspondence between the graphs and the signs of the coefficients k And b.

ODDS

1) k b 2) k > 0, b > 0

3) k b > 0

4) k > 0, b Provide your answer as a sequence of numbers without spaces or commas in the order specified.

ABIN

Solution.

x, then the coefficient k b x b

Thus, the following coefficients correspond to the graphs: A - 1, B - 3, C - 4.

Answer: 134.

Answer: 134

The figure shows graphs of functions of the form y = khx + b k And b and graphs.

ODDS

ABIN

Solution.

If the function value increases with increasing x, then the coefficient k is positive; if it decreases, it is negative. Meaning b corresponds to the value of the function at the point x= 0, therefore, if the graph intersects the ordinate axis above the abscissa axis, then the value b positive, if below the x-axis - negative.

Answer: 231.

Answer: 231

ODDS

Write down the numbers in your answer, arranging them in the order corresponding to the letters:

ABIN

Solution.

If the function value increases with increasing x, then the coefficient k is positive; if it decreases, it is negative. Meaning b corresponds to the value of the function at the point x= 0, therefore, if the graph intersects the ordinate axis above the abscissa axis, then the value b positive, if below the x-axis - negative.

Thus, the following coefficients correspond to the graphs: A - 3, B - 2, C - 1.

Answer: 321.

Vm kv (Kuluevo) 23.02.2016 18:22

Graph 4 is suitable for B, not graph 2, because we see that on graph 4 k>0 and b>0, and on graph 2 k<0 и b>0.

Irina Safiulina

Good afternoon

On the 4k chart

Evgeny Pugachev 28.05.2016 12:26

Graph 3 is suitable for A, Graph 1 for B, because b>0, and Graph 2 for B, because b<0

The figure shows graphs of functions of the form. Establish a correspondence between the signs of the coefficients and and the graphs.

ODDS

Write down the numbers in your answer, arranging them in the order corresponding to the letters:

ABIN

Answer: 231

The figure shows graphs of functions of the form. Establish a correspondence between the graphs and signs of the coefficients and

ODDS

Write down the numbers in your answer, arranging them in the order corresponding to the letters:

ABIN

Solution.

If the function value increases with increasing x, then the coefficient k is positive; if it decreases, it is negative. Meaning b corresponds to the value of the function at the point x= 0, therefore, if the graph intersects the ordinate axis above the abscissa axis, then the value b positive, if below the x-axis - negative.

Thus, the following coefficients correspond to the graphs: A - 2, B - 1, C - 4.

Answer: 214.

Answer: 214

The figure shows graphs of functions of the form y = kx + b. Match the signs of the coefficients k And b and function graphs.

Charts

Odds

Solution.

If the function value increases with increasing x, then the coefficient k is positive; if it decreases, it is negative. Meaning b corresponds to the value of the function at the point x= 0, therefore, if the graph intersects the ordinate axis above the abscissa axis, then the value b positive, if below the x-axis - negative. Thus, the following graphs correspond to the coefficients: A - 2, B - 1, C - 3.

Answer: 213.

y = kx + b k And b.

GRAPHICS
A)B)IN)
ODDS
1) k b > 02) k > 0, b > 0 3) k b4) k > 0, b

The figure shows graphs of functions of the form y = kx + b. Establish a correspondence between function graphs and coefficient signs k And b.

GRAPHICS
A)B)IN)
ODDS
1) k > 0, b > 0 2) k b > 03) k > 0, b 4) k b

The figure shows graphs of functions of the form y = kx + b. Establish a correspondence between function graphs and coefficient signs k And b.

GRAPHICS
A)B)IN)
ODDS
1) k b > 02) k b3) k > 0, b 4) k > 0, b > 0

The figure shows graphs of functions of the form y = kx + b. Establish a correspondence between function graphs and coefficient signs k And b.

GRAPHICS
A)B)IN)
ODDS
1) k b2) k > 0, b 3) k b > 04) k > 0, b > 0

The figure shows graphs of functions of the form y = kx + b. Establish a correspondence between function graphs and coefficient signs k And b.

GRAPHICS
A)B)IN)
ODDS
1) k b2) k b > 03) k > 0, b 4) k > 0, b > 0

The figure shows graphs of functions of the form y = kx + b. Establish a correspondence between function graphs and coefficient signs k And b.

GRAPHICS
A)B)IN)
ODDS
1) k > 0, b 2) k b3) k b > 04) k > 0, b > 0

The figure shows graphs of functions of the form y = kx + b. Establish a correspondence between function graphs and coefficient signs k And b.

GRAPHICS
A)B)IN)
ODDS
1) k b > 02) k > 0, b 3) k > 0, b > 0 4) k b

The figure shows graphs of functions of the form y = kx + b. Establish a correspondence between function graphs and coefficient signs k And b.

GRAPHICS
A)B)IN)
ODDS
1) k > 0, b > 0 2) k b > 03) k b4) k > 0, b

The figure shows graphs of functions of the form y = kx + b. Establish a correspondence between function graphs and coefficient signs k And b.

GRAPHICS
A)B)IN)
ODDS
1) k b2) k > 0, b 3) k b > 04) k > 0, b > 0

The figure shows graphs of functions of the form y = kx + b. Establish a correspondence between function graphs and coefficient signs k And b.

GRAPHICS
A)B)IN)
ODDS
1) k b2) k > 0, b > 0 3) k b > 04) k > 0, b

The figure shows graphs of functions of the form y = kx + b. Establish a correspondence between function graphs and coefficient signs k And b.

GRAPHICS
A)B)IN)

Write down the numbers in your answer, arranging them in the order corresponding to the letters:

ABIN

Solution.

If the function value increases with increasing x, then the coefficient k is positive; if it decreases, it is negative. Meaning b corresponds to the value of the function at the point x= 0, therefore, if the graph intersects the ordinate axis above the abscissa axis, then the value b positive, if below the x-axis - negative.

Thus, the following graphs correspond to the coefficients: A - 2, B - 1, C - 3.

Answer: 213.

Answer: 213

The figure shows graphs of functions of the form y = kx + b. Match the signs of the coefficients k And b and function graphs.

Charts

Odds

Solution.

If the function value increases with increasing x, then the coefficient k is positive; if it decreases, it is negative. Meaning b corresponds to the value of the function at the point x= 0, therefore, if the graph intersects the ordinate axis above the abscissa axis, then the value b positive, if below the x-axis - negative.

Thus, the following graphs correspond to the coefficients: A - 4, B - 3, C - 1.

Answer: 431.

Answer: 431

The figure shows graphs of functions of the form y = kx + b. Match the signs of the coefficients k And b and function graphs.

Charts

Odds

Solution.

If the function value increases with increasing x, then the coefficient k is positive; if it decreases, it is negative. Meaning b corresponds to the value of the function at the point x= 0, therefore, if the graph intersects the ordinate axis above the abscissa axis, then the value b positive, if below the x-axis - negative.

Thus, the following graphs correspond to the coefficients: A - 2, B - 4, C - 3.

Answer: 243.

Answer: 243

The figure shows graphs of functions of the form y = kx + b. Match the signs of the coefficients k And b and function graphs.

Charts

Odds

Solution.

If the function value increases with increasing x, then the coefficient k is positive; if it decreases, it is negative. Meaning b corresponds to the value of the function at the point x= 0, therefore, if the graph intersects the ordinate axis above the abscissa axis, then the value b positive, if below the x-axis - negative.

Answer: 132.

Answer: 132

The figure shows graphs of functions of the form y = kx + b. Match the signs of the coefficients k And b and function graphs.

Charts

Odds

Solution.

If the function value increases with increasing x, then the coefficient k is positive; if it decreases, it is negative. Meaning b corresponds to the value of the function at the point x= 0, therefore, if the graph intersects the ordinate axis above the abscissa axis, then the value b positive, if below the x-axis - negative.

Thus, the following graphs correspond to the coefficients: A - 1, B - 3, C - 2.

Answer: 132.

Answer: 132

Establish a correspondence between the graphs of functions and the formulas that define them.

ABIN

Solution.

If the function value increases with increasing x, then the coefficient k is positive; if it decreases, it is negative. Meaning b corresponds to the value of the function at the point x b positive, if below the x-axis - negative. Thus, A - 2, B - 3, C - 1

Answer: 231.

Answer: 231

ODDS

GRAPHICS

Solution.

If the function value increases with increasing x, then the coefficient k is positive; if it decreases, it is negative. Meaning b corresponds to the value of the function at the point x= 0. Therefore, if the graph intersects the ordinate axis above the abscissa axis, then the value b positive, if below the x-axis - negative. Thus, the following coefficients correspond to the graphs: A - 2, B - 3, C -1.

Answer: 231.

Answer: 231

The figures show graphs of functions of the form. Establish a correspondence between the signs of the coefficients and and the graphs of the functions.

ODDS

GRAPHICS

Write down the numbers in your answer, arranging them in the order corresponding to the letters:

ABIN

Solution.

If the function value increases with increasing x, then the coefficient k is positive; if it decreases, it is negative. Meaning b corresponds to the value of the function at the point x= 0, therefore, if the graph intersects the ordinate axis above the abscissa axis, then the value b positive, if below the x-axis - negative.

Answer: 312.

Answer: 312

The figure shows graphs of functions of the form. Establish a correspondence between the signs of the coefficients and and the graphs of the functions.

ODDS

GRAPHICS

Write down the numbers in your answer, arranging them in the order corresponding to the letters:

ABIN

Solution.

If the function value increases with increasing x, then the coefficient k is positive; if it decreases, it is negative. Meaning b corresponds to the value of the function at the point x= 0, therefore, if the graph intersects the ordinate axis above the abscissa axis, then the value b positive, if below the x-axis - negative.

Thus, the following coefficients correspond to the graphs: A - 1, B - 3, C - 2.

Answer: 132.

Answer: 132

The figure shows graphs of functions of the form y = khx + b. Match the signs of the coefficients k And b and function graphs.

ODDS

GRAPHICS

Write down the numbers in your answer, arranging them in the order corresponding to the letters:

ABIN

Solution.

If the function value increases with increasing x, then the coefficient k is positive; if it decreases, it is negative. Meaning b corresponds to the value of the function at the point x= 0, therefore, if the graph intersects the ordinate axis above the abscissa axis, then the value b positive, if below the x-axis - negative.

Thus, the following coefficients correspond to the graphs: A - 3, B - 1, C - 2.

Answer: 312

Answer: 312

The figures show graphs of functions of the form. Establish a correspondence between the signs of the coefficients and and the graphs of the functions.

ODDS

GRAPHICS

In the table, under each letter, indicate the corresponding number.

ABIN

Solution.

If the function value increases with increasing x, then the coefficient k is positive; if it decreases, it is negative. Meaning b corresponds to the value of the function at the point x= 0, therefore, if the graph intersects the ordinate axis above the abscissa axis, then the value b positive, if below the x-axis - negative.

Answer: 213.

Answer: 213

The figures show graphs of functions of the form. Establish a correspondence between the signs of the coefficients and and the graphs of the functions.

ODDS

GRAPHICS

In the table, under each letter, indicate the corresponding number.

Solution.

If the function value increases with increasing x, then the coefficient k is positive; if it decreases, it is negative. Meaning b corresponds to the value of the function at the point x= 0, therefore, if the graph intersects the ordinate axis above the abscissa axis, then the value b positive, if below the x-axis - negative.

Thus, the following graphs correspond to the coefficients: A - 2, B - 3, C -1.

Answer: 231.

Answer: 231

The figures show graphs of functions of the form. Establish a correspondence between the signs of the coefficients and and the graphs of the functions.

ODDS

GRAPHICS

In the table, under each letter, indicate the corresponding number.

Write down the numbers in your answer, arranging them in the order corresponding to the letters:

ABIN

Solution.

If the function value increases with increasing x, then the coefficient k is positive; if it decreases, it is negative. Meaning b corresponds to the value of the function at the point x= 0, therefore, if the graph intersects the ordinate axis above the abscissa axis, then the value b positive, if below the x-axis - negative.

Thus, the following graphs correspond to the coefficients: A - 3, B - 2, C -1.

Answer: 321.

Answer: 321

The figures show graphs of functions of the form. Establish a correspondence between the signs of the coefficients and and the graphs of the functions.

ODDS

GRAPHICS

In the table, under each letter, indicate the corresponding number.

Write down the numbers in your answer, arranging them in the order corresponding to the letters:

ABIN

Solution.

If the function value increases with increasing x, then the coefficient k is positive; if it decreases, it is negative. Meaning b corresponds to the value of the function at the point x= 0, therefore, if the graph intersects the ordinate axis above the abscissa axis, then the value b positive, if below the x-axis - negative.

Thus, the following graphs correspond to the coefficients: A - 1, B - 2, C -3.

Answer: 123.

Answer: 123

The figures show graphs of functions of the form. Establish a correspondence between the signs of the coefficients and and the graphs of the functions.

ODDS

GRAPHICS

In the table, under each letter, indicate the corresponding number.

Write down the numbers in your answer, arranging them in the order corresponding to the letters:

ABIN

Solution.

If the function value increases with increasing x, then the coefficient k is positive; if it decreases, it is negative. Meaning b corresponds to the value of the function at the point x= 0, therefore, if the graph intersects the ordinate axis above the abscissa axis, then the value b positive, if below the x-axis - negative.

Thus, the following graphs correspond to the coefficients: A - 2, B - 3, C -1.

Answer: 231.

Answer: 231

The figures show graphs of functions of the form. Establish a correspondence between the signs of the coefficients and and the graphs of the functions.

ODDS

GRAPHICS

Write down the numbers in your answer, arranging them in the order corresponding to the letters:

ABIN

Solution.

If the function value increases with increasing x, then the coefficient k is positive; if it decreases, it is negative. Meaning b corresponds to the value of the function at the point x= 0, therefore, if the graph intersects the ordinate axis above the abscissa axis, then the value b positive, if below the x-axis - negative.

Thus, the following graphs correspond to the coefficients: A - 1, B - 3, C -2.

Answer: 132.

Answer: 132

The figures show graphs of functions of the form. Establish a correspondence between the signs of the coefficients and and the graphs of the functions.

ODDS

GRAPHICS

Write down the numbers in your answer, arranging them in the order corresponding to the letters:

ABIN

Solution.

If the function value increases with increasing x, then the coefficient k is positive; if it decreases, it is negative. Meaning b corresponds to the value of the function at the point x= 0, therefore, if the graph intersects the ordinate axis above the abscissa axis, then the value b positive, if below the x-axis - negative.

Thus, the following graphs correspond to the coefficients: A - 2, B - 3, C -1.

Answer: 231.

Answer: 231

The figures show graphs of functions of the form. Establish a correspondence between the signs of the coefficients and and the graphs of the functions.

ODDS

GRAPHICS

In the table, under each letter, indicate the corresponding number.

ABIN

Solution.

If the function value increases with increasing x, then the coefficient k is positive; if it decreases, it is negative. Meaning b corresponds to the value of the function at the point x= 0, therefore, if the graph intersects the ordinate axis above the abscissa axis, then the value b positive, if below the x-axis - negative.

Thus, the following graphs correspond to the coefficients: A - 2, B - 1, C -3.

Answer: 213.

Answer: 213

The figures show graphs of functions of the form. Establish a correspondence between the signs of the coefficients and and the graphs of the functions.

ODDS

GRAPHICS

In the table, under each letter, indicate the corresponding number.

Solution.

If the function value increases with increasing x, then the coefficient k is positive; if it decreases, it is negative. Meaning b corresponds to the value of the function at the point x= 0, therefore, if the graph intersects the ordinate axis above the abscissa axis, then the value b positive, if below the x-axis - negative.

Thus, the following graphs correspond to the coefficients: A - 3, B - 1, C -2.

Answer: 312.

Answer: 312

The figures show graphs of functions of the form. Establish a correspondence between the signs of the coefficients and and the graphs of the functions.

ODDS

GRAPHICS

In the table, under each letter, indicate the corresponding number.

Write down the numbers in your answer, arranging them in the order corresponding to the letters:

ABIN

Solution.

If the function value increases with increasing x, then the coefficient k is positive; if it decreases, it is negative. Meaning b corresponds to the value of the function at the point x= 0, therefore, if the graph intersects the ordinate axis above the abscissa axis, then the value b positive, if below the x-axis - negative.

As practice shows, tasks on the properties and graphs of a quadratic function cause serious difficulties. This is quite strange, because they study the quadratic function in the 8th grade, and then throughout the first quarter of the 9th grade they “torment” the properties of the parabola and build its graphs for various parameters.

This is due to the fact that when forcing students to construct parabolas, they practically do not devote time to “reading” the graphs, that is, they do not practice comprehending the information received from the picture. Apparently, it is assumed that, after constructing a dozen or two graphs, a smart student himself will discover and formulate the relationship between the coefficients in the formula and appearance graphic arts. In practice this does not work. For such a generalization, serious experience in mathematical mini-research is required, which most ninth-graders, of course, do not possess. Meanwhile, the State Inspectorate proposes to determine the signs of the coefficients using the schedule.

We will not demand the impossible from schoolchildren and will simply offer one of the algorithms for solving such problems.

So, a function of the form y = ax 2 + bx + c called quadratic, its graph is a parabola. As the name suggests, the main term is ax 2. That is A should not be equal to zero, the remaining coefficients ( b And With) can equal zero.

Let's see how the signs of its coefficients affect the appearance of a parabola.

The most simple dependency for the coefficient A. Most schoolchildren confidently answer: “if A> 0, then the branches of the parabola are directed upward, and if A < 0, - то вниз". Совершенно верно. Ниже приведен график квадратичной функции, у которой A > 0.

y = 0.5x 2 - 3x + 1

IN in this case A = 0,5

And now for A < 0:

y = - 0.5x2 - 3x + 1

In this case A = - 0,5

Impact of the coefficient With It's also pretty easy to follow. Let's imagine that we want to find the value of a function at a point X= 0. Substitute zero into the formula:

y = a 0 2 + b 0 + c = c. It turns out that y = c. That is With is the ordinate of the point of intersection of the parabola with the y-axis. Typically, this point is easy to find on the graph. And determine whether it lies above zero or below. That is With> 0 or With < 0.

With > 0:

y = x 2 + 4x + 3

With < 0

y = x 2 + 4x - 3

Accordingly, if With= 0, then the parabola will necessarily pass through the origin:

y = x 2 + 4x


More difficult with the parameter b. The point at which we will find it depends not only on b but also from A. This is the top of the parabola. Its abscissa (axis coordinate X) is found by the formula x in = - b/(2a). Thus, b = - 2ax in. That is, we act in the following way: on the graph we find the vertex of the parabola, determine the sign of its abscissa, that is, look to the right of zero ( x in> 0) or to the left ( x in < 0) она лежит.

However, that's not all. We also need to pay attention to the sign of the coefficient A. That is, look at where the branches of the parabola are directed. And only after that, according to the formula b = - 2ax in determine the sign b.

Let's look at an example:

The branches are directed upwards, which means A> 0, the parabola intersects the axis at below zero, that is With < 0, вершина параболы лежит правее нуля. Следовательно, x in> 0. So b = - 2ax in = -++ = -. b < 0. Окончательно имеем: A > 0, b < 0, With < 0.

“Drawings for slides” - Optional course “World of Multimedia Technologies”. Drawings on slides. C) you can transfer the drawing by grabbing the middle with the mouse. Inserting pictures onto a slide. Municipal educational institution average comprehensive school No. 5. 95% of information is perceived by a person through the organs of vision...

“Functions and their graphs” - 3. Tangent function. Trigonometric. The function is defined and continuous on the entire set real numbers. Definition: Numeric function, given by the formula y = cos x, called cosine. 4.Cotangent function. At the point x = a the function may or may not exist. Definition 1. Let the function y = f(x) be defined on an interval.

"Functions of Several Variables" - Greatest and smallest value functions. Weierstrass's theorem. Internal and boundary points. Limit of a function of 2 variables. Function graph. Theorem. Continuity. Limited area. Open and closed area. Derivatives of higher orders. Partial derivatives. Partial increments of a function of 2 variables.

“3D drawings on asphalt” - Kurt began creating his first works at the age of 16 in Santa Barbara, where he became addicted to street art. 3d drawings on asphalt. Kurt Wenner is one of the most famous street artists who draws 3D drawings on asphalt using regular crayons. USA. As a young man, Kurt Wenner worked as an illustrator for NASA, where he created initial images of future spacecraft.

“Topic Function” - If students work differently, then the teacher should work with them differently. It is necessary to find out not what the student does not know, but what he knows. Generalization. Synthesis. Unified State Exam results mathematics. Program elective course. Association. Educational and thematic plan(24 hours). Analogy. If a student surpasses a teacher, this is the teacher’s happiness.

5. Monomial The product of numeric and alphabetic factors is called. Coefficient is called the numerical factor of a monomial.

6. To write a monomial in standard form, necessary: 1) Multiply the numerical factors and put their product in first place; 2) Multiply powers with on the same grounds and place the resulting product after the numerical factor.

7. A polynomial is called algebraic sum several monomials.

8. To multiply a monomial by a polynomial, You need to multiply the monomial by each term of the polynomial and add the resulting products.

9. To multiply a polynomial by a polynomial, It is necessary to multiply each term of one polynomial by each term of another polynomial and add the resulting products.

10. Through any two points you can draw a straight line, and only one.

11. Two straight lines or have only one common point, or do not have common points.

12. Two geometric figures are called equal if they can be combined by overlapping.

13. The point of a segment dividing it in half, i.e. into two equal to the segment, is called the midpoint of the segment.

14. A ray emanating from the vertex of an angle and dividing it into two equal angles, is called the angle bisector.

15. The rotated angle is 180°.

16. An angle is called right if it is equal to 90°.

17. An angle is called acute if it is less than 90°, that is, less than a right angle.

18. An angle is called obtuse if it is more than 90°, but less than 180°, that is, more than a right angle, but less than a straight angle.

19. Two angles in which one side is common, and the other two are continuations of one another, are called adjacent.

20. Sum adjacent corners equal to 180°.

21. Two angles are called vertical if the sides of one angle are continuations of the sides of the other.

22. Vertical angles are equal.


23. Two intersecting lines are called perpendicular (or mutually

perpendicular) if they form four right angles.

24. Two lines perpendicular to a third do not intersect.

25. Factor the polynomial- means to represent it as a product of several monomials and polynomials.

26. Methods of factoring a polynomial:

a) putting the common factor out of brackets,

b) use of abbreviated multiplication formulas,

c) method of grouping.

27.To factor a polynomial by taking the common factor out of brackets, you need:

a) find this one common multiplier,

b) take it out of brackets,

c) divide each term of the polynomial by this factor and add the resulting results.

Signs of equality of triangles

1) If two sides and the angle between them of one triangle are respectively equal to two sides and the angle between them of another triangle, then such triangles are congruent.

2) If a side and two adjacent angles of one triangle are respectively equal to the side and two adjacent angles of another triangle, then such triangles are congruent.

3) If three sides of one triangle are respectively equal to three sides of another triangle, then such triangles are congruent.

Educational minimum

1. Factorization using abbreviated multiplication formulas:

a 2 – b 2 = (a – b) (a + b)

a 3 – b 3 = (a – b) (a 2 + ab + b 2)

a 3 + b 3 = (a + b) (a 2 – ab + b 2)

2. Abbreviated multiplication formulas:

(a + b) 2 =a 2 + 2ab + b 2

(a – b) 2 = a 2 – 2ab + b 2

(a + b) 3 =a 3 + 3a 2 b + 3ab 2 + b 3

(a – b) 3 = a 3 – 3a 2 b + 3ab 2 – b 3

3. The segment connecting the vertex of a triangle with the midpoint of the opposite side is called median triangle.

4. A perpendicular drawn from a vertex of a triangle to a line containing the opposite side, called height triangle.

5. IN isosceles triangle the angles at the base are equal.

6. In an isosceles triangle, the bisector drawn to the base is the median and altitude.

7. Circumference called geometric figure, consisting of all points of the plane located on given distance from this point.

8. A segment connecting the center with any point on the circle is called radius circle .

9. A segment connecting two points on a circle is called chord.

A chord passing through the center of a circle is called diameter

10. Direct proportionality y = kx , Where X – independent variable, To - Not equal to zero number ( To – proportionality coefficient).

11. Direct proportionality graph is a straight line passing through the origin of coordinates.

12. Linear function is a function that can be given by the formula y = kx + b , Where X – independent variable, To And b - some numbers.

13. Schedule linear function - this is a straight line.

14 X – function argument (independent variable)

at – function value (dependent variable)

15. At b=0 the function takes the form y=kx, its graph passes through the origin.

At k=0 the function takes the form y=b, its graph is a horizontal line passing through the point ( 0;b).

Correspondence between the graphs of a linear function and the signs of the coefficients k and b

1. Two straight lines in a plane are called parallel, if they don't intersect.