First, find the domain of the function. The scope includes all valid arguments of the function, that is, those arguments for which the function makes sense. It is clear that the denominator of the fraction cannot be zero, under the root cannot be a negative number. The base of the logarithm must be positive and not equal to one. The expression under the logarithm must be positive. Restrictions on the domain of the function can be imposed and the condition of the problem.
Consider how the domain of the function affects the set of values that a function can take.
The set of values of a linear function represents the set of all real numbers (x belongs R), as a direct set of a linear equation, infinite.
In the case of a quadratic function find the value of the vertex of the parabola (x0=-b/a, y0=y(x0). If the branches of the parabola are directed upwards (a>0), then the set of values of the function are all y>y0. If the branches of the parabola are directed downwards (a<0), the range of functions defined by inequalities y
The set of values of the cubic function, the set of real numbers (x belongs R). In General, the range of any function with an odd exponent (5, 7, ...) is a field of real numbers.
The set of values of exponential function (y=a^x, where a is a positive number) is all numbers greater than zero.
To find the set of values of linear-fractional or fractional-rational function, you need to find the equations of the horizontal asymptotes. Find the value of x at which the denominator vanishes. Imagine how the schedule would look like. Sketch the graph. Based on this, define the set of values of the function.
The set of values of trigonometric functions sine and cosine are strictly limited. Sine and cosine on the module cannot exceed unity. But the value of tangent and cotangent can be anything.
If the problem is to find the set of values of the function on the given interval of values of the argument, consider the function specifically at this segment.
While many of the function values is useful to determine the intervals of monotonicity of the function - ascending & descending. This allows us to understand the behavior of the function.
The plotting functions (or at least sketch graphics will assist you to define a set of function values. Consider the type of function with which you are dealing (logarithmic, rational, trigonometric, linear, quadratic, etc.).