A relation is a group of values bearing inputs and outputs. Normally, the output will be influenced by the value and quality of inputs. For example, when going to a store to buy goods for the manufacture of fruit yogurt, there will be a relation. This is because the buyer will have to put in funds to obtain the raw materials to make the fruit yogurt, which are the output. Therefore, relations often have dependent outputs because the input must be present for the output to occur. A function, on the other hand, is where there is one input, yet there is only one output. For example, assuming the store in the first example sold the ingredients during a sale. When the store is no longer offering the sale and every output is dependent on the singular input, then it is said that this is a function.
In a graph having values of x and y , a domain is the total numbers of values on the x axis where values satisfy the function. In other words, the values which make the function work constitute the domain. Therefore, two main things need to be considered during this, namely that the denominator of the fraction cannot be zero and that the number under the square root sign, if any, must be a positive value. Therefore, determining the domain value is quite easy so long as one checks the x axis value while avoiding negative values under the square root sign and zero as denominators for fractions. The range, on the other hand, is all sets of values on the y -axis, which can be substituted for all acceptable domain values (Stewart, 2001). In other words, when the domain values are obtained, then substituting the y-axis values enables one to get the range.
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Having determined this, examining the value on the graph to determine whether it is a function is relatively simple. The vertical line test is the simplest method of determining whether value on a graph is a function. In this case, the learner must check to see whether the representation on a graph is a straight line. Where a straight line is present, then it shows that every one input produces a single output. Therefore, the value will be a function. However, where the line is not straight, it shows that there is more or less than one output for each input. Where the tangent of the line is one, then the line is straight and therefore values on the graph are a function.
Figure 1 : Function vs. non-function graph
References
Stewart, J. (2001). Calculus: Concepts and Contexts (2nd ed.). Pacific Grove: Brooks/Cole.
