Finding the Domain of a Function (not from a graph)

Aggressive symbols - representing radical symbols, simplifying free radicals, and converting fractional indexes to radical symbols

Another way to identify the scope of the field and function is to use graphics. Since the field refers to the possible set of input values, the field of the graph contains all input values ​​displayed on the x axis. The range is a collection of possible output values ​​displayed on the y axis. Note that if the graph continues to be displayed beyond a part of the graph, the field and range may be larger than the displayed value. See Figure 6. Since the graph extends horizontally from -5 to the right without a boundary, the field is \ left. Since the vertical range of the graph is a range value of less than or equal to 5, the range is \ left (\ mathrm {- \ infty}, 5 \ right] The fields and ranges are always written from small values ​​to large values. In the case of scope, it is used from the bottom of the figure to the top of the figure.

Functions can be defined using words, symbols, graphics, tables, or ordered pairs, but in both cases the parts are the same. The field is an input, an independent value - it is the content of the function. Scope is output according to the value - it is coming out. Domains and ranges can be restricted to a number of distinct values ​​or infinite numbers and more in all places.

Finding a range is a little more troublesome than finding a domain. We strongly recommend using a graph calculator to accurately grasp the function. However, if not, we recommend that you draw some basic functions manually. Either way, in order to correctly describe the scope of the function, it is necessary to clearly understand the appearance of the graphic. The first thing I noticed was that this question had no square root symbol or denominator. You can not use this function to get a square root or negative divide by zero, so this is fine. It is easy to say that this field is an x ​​value because there is no x value that might invalidate the output of the function. However, it would be much better to write it in group expressions or section expressions.