Let two functions be set: y=y(x) and y=y' (x). These functions describe some locus on the coordinate plane. It can be straight lines, hyperboles, parabolas, curves without a certain name. How to find points of intersection of these lines and their coordinate?
Instruction
1. Express an argument from any function x. For x substitute the received expression in the second function.
2. From the turned-out equation find x. It will be coordinates of points of intersection of functions. If there are no such values x which would satisfy to the equation, so functions are not crossed. If the unique numerical value x is found, so functions are crossed only in one point. If variable x has several values, then functions are crossed in several points.
3. Find value of function for each of points of intersection (in both functions these values have to coincide in number therefore choose that function which value it is simpler to find). You received full coordinates of points of intersection.
4. Write down coordinates of points of intersection in a standard look: (value of an argument in a point, value of function in a point).
5. Do not forget about ranges of definition of functions. Can happen so that the presented functions have no general ranges of definition. In that case, further search of points of intersection does not make sense. And can happen so that only one point is the general for ranges of definition of functions. In that case, it is necessary to consider only it one. For example, the ""root from x"" functions and ""a root from minus x"". Both of these functions are defined only in a point zero. The same point will be also a point of intersection of functions. Besides these extreme cases, still the set of variations is possible. Anyway, the range of definition of functions should be considered.
6. If it is necessary to find function points of intersection with abscissa axis (Ox), consider it as y=0 function. Oy describes x=0 equation.
7. If it is required to find points of intersection in a task in the geometrical way, construct function graphs. Find approximate value of coordinates of points in which these functions are crossed on graphics. Write down the answer.