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.

How to define a function according to the schedule
As for the graphics of the derivative to graph functions
How to solve a function
How to find the value of the function

Instruction

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.

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.

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.

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.

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.

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.

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