Instruction

1

If the graph is a straight line passing through the origin and forming with the axis OX the angle α (the angle of inclination of a straight line to the positive half-axis OX). The function that describes this line will have the form y = kx. The coefficient of proportionality k is equal to tg α. If the line passes through 2 nd and 4-th quadrant, k < 0, and the function is decreasing if in the 1st and 3rd, then k > 0 and a function increases.Let the graph is a straight line, arranged in different ways relative to the axes of coordinates. It is a linear function, and it has the form y = kx + b, where variables x and y are in the first degree, and k and b can take both positive and negative values or zero. Video is parallel to the line y = kx cuts and on the y-axis |b| units. A line parallel to the x-axis, then k = 0 if the y-axis, the equation has the form x = const.

2

A curve consisting of two branches, located in different quarters and symmetric about the origin, is called a hyperbola. This graph expresses the inverse relationship of the variable y from x and is described by the equation y = k/x. Here k ≠ 0 is the coefficient of inverse proportionality. In this case, if k > 0, the function decreases; if k < 0 the function is increasing. Thus, the domain of the function is the entire number line except x = 0. The branches of the hyperbola approach the coordinate axes as their asymptotes. With decreasing k the branches of the hyperbola are more "pressed" into the coordinate angles.

3

A quadratic function has the form y = ax2 + bx + C, where a, b and c values constant and a 0. If the condition b = C = 0, a function equation looks like y = ax2 (the simplest case of a quadratic function), and its graph is a parabola passing through the origin. The graph of the function y = ax2 + bx + C has the same form as the simplest case of functions, however, its peak (the point of intersection of the parabola with the axis OY) lies not in the origin.

4

A parabola is also the graph of the exponential function expressed by the equation y = xⁿ, if n is any even number. If n is any odd number, the graph of this exponential function will have the form of a cubic parabola.

If n is any negative number, a function equation takes the form. The graph of the function with odd n is a hyperbola, and if n is even their branches are symmetric about the axis Oy.

If n is any negative number, a function equation takes the form. The graph of the function with odd n is a hyperbola, and if n is even their branches are symmetric about the axis Oy.

# Advice 2: How to define a function according to the schedule

Coordinate of any point on the plane is determined by two variables: on the x-axis and the y-axis. A set of such points and represents the graph of the function. On it you see a change in the Y value depending on changing the value of X. you can Also determine in which area (gap) the function increases and what decreases.

Instruction

1

What can we say about a function if its graph is a straight line? Let's see if this video passes through the origin of coordinates (that is, one where the values of X and Y is equal to 0). If held, such a function is described by the equation y = kx. It is easy to understand that the larger the value of k, the closer to the y-axis will be located this video. And the Y-axis actually corresponds to an infinitely large value of k.

2

Look at the direction of the function. If it goes "lower left – top right", that is, the 3rd and the 1st quadrant, it is increasing, if "top left to right down" (via the 2nd and 4th quarters), it is waning.

3

When video does not pass through the origin, it is described by the equation y = kx + b. Video crosses the y-axis at the point where y = b and y value can be positive or negative.

4

A function is called a parabola, if is described by the equation y = x^n, and its appearance depends on the value of n. If n is any even number (the simplest case of a quadratic function y = x^2) function graph is a curve passing through the origin and through the point with coordinates (1;1), (-1;1), since the unit in any degree will remain one. All values of y corresponding to any value X other than zero, can only be positive. The function is symmetric about the Y-axis and its graph is 1-St and 2-nd coordinate quarters. It is easy to understand that the larger the value of n, the close graph is to the y-axis.

5

If n is an odd number, the graph of this function is a cubic parabola. Curve is located in the 1st and 3rd coordinate quadrants, symmetrical with respect to the Y-axis and passes through the origin and through the point (-1;-1), (1;1). When a quadratic function is an equation y = ax^2 + bx + c form of the parabola coincides with the form in the simplest case (y = x^2), but its peak is not at the point of origin.

6

A function is called a hyperbola, if it is described by the equation y = k/x. It is easy to see that when the value of x tends to 0, the value of y increases to infinity. The function graph is a curve consisting of two branches which are located in different coordinate quarters.