Advice 1: How to solve a function

To compute the value functions are used different techniques: using the formula, where it is set, graph or table. All these methods have a certain algorithm execution.
how to solve a function
Instruction
1
If you want to find the value of the function, using the formula, substitute in this formula instead of the argument (x), its valid values, i.e. values that are included in its scope. For this you need to find a domain of valid values for this function.
2
To find the domain of the function, determine what type she has. If the function of the form y = a/b, its domain would be all values except zero. The number a is any number. To find the area of function definition, radical expressions, provided the even indicator, this expression must be greater than or equal to zero. Finding the domain of the function the same expression, but with an odd index, keep in mind that x can be any number in that case, if the radical expression is not a fraction. Finding the domain of logarithmic functions, use the rule that expression which stands under the sign of logarithm must be a positive value.
3
Finding the domain of the function, go to it. For example, to solve the function: y = 2.5 x – 10 when x = 100, substitute in this formula x is the number 100. This operation will be as follows: y = 2.5 x 100 – 10; y = 240. This number is the required value of the function.
4
To find the value of the function using the graph, put in a rectangular coordinate system on the axis OX of the value of the argument (the point corresponding to the argument). Then, from the point of the guide perpendicular to the intersection of it with the plot function. From the resulting points of intersection of the perpendicular with the plot function, we drop a perpendicular on the axis OU. The base is constructed perpendicular will meet the desired value of the function.
5
If the function is set to table, then each argument value there is a corresponding value of the function.

Advice 2 : As for the graphics of the derivative to graph functions

If the graph of the derivative is explicitly expressed signs, it is possible to speculate about the behavior of the integral. When plotting the function check of the findings by the characteristic points.
As for the graphics of the derivative to graph functions
Instruction
1
If the graph of the derivative should be straight and parallel to the axis OX, the equation Y' = k, then the sought-for function Y = k*x. If the graph of the derivative is a straight line passing at an angle to the numeric-axis, the graph of the parabola. If the graph of the derivative is similar to a hyperbole, even before his research, we can assume that the integral is a function of the natural logarithm. If the graph of the derivative — sine wave, the function is the cosine of the argument.
2
If the graph of the derivative is a straight line, then its equation in General form we can write Y'=k*x+b. To determine the coefficient k in a variable x will be a parallel schedule straight line through the origin. Remove this auxiliary graph of the x and y coordinates of an arbitrary point and calculate k= y/x. Sign k install in the direction of the graph of the derivative — if with the increase in the value of the argument graph rises, hence k>0. The value of the intercept b is equal to the value of Y' when x=0.
3
Determine the formula of a function compiled the equation of the derivative:
Y=k/2 * x2+bx+C

Free member with to find the schedule of the derivative is impossible. The position of the function along the Y-axis is not fixed. Points plot the resulting function is a parabola. The branches of the parabola are directed upwards if k>0 and down if k<0.
4
The graph of the derivative of exponential function coincides with the graph of the function, since the differentiation of the exponential function does not change. The control point on the graph has coordinates (0, 1), since any number to the power of zero equal to one.
5
If the graph of the derivative is the hyperbola with branches in the first and third quarters of the coordinate axes, the equation of the derivative Y' = 1/x. Therefore the integral will be a function of the natural logarithm. The reference point when plotting the function (1,0) and (e, 1).
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