Question

(pleasseeee do not take a picture, need this typed out)

What is the difference between a relation and function? Discuss how to find the domain and range of a function. What test can you use to identify a function on a graph? Explain how to use it. Create one function and ask your peers to find the domain and range. Ask them to discuss the shape of the graph. Return to the Discussion to check your peers’ understanding and offer help as needed. Be sure to post the answer at the close of the module.

Answer 1

Every function is a relation whereas a relation may or may not be a function.

A relation comprises two sets of elements called inputs and outputs and establishes a relationship between these 2 sets of values, i.e. the inputs and the outputs. In case of a relation, it is not necessary that each input be related to only ne output. For example, we can consider a relation that corresponds a mother to her children. Here, if the mother has more than one child, the relation assigns more than one value of output to each input.

A function is a relation where each input is related to exactly one output. With this condition, a function may also be defined as a set of ordered pairs. A function may also be described as a correspondence between the set of inputs (called the domain) and the set of outputs (called the range) such that to each element of the domain, is assigned to exactly one element of the range. For example, we can consider a relation that corresponds a mother to her only child. Here, the relation assigns only one value of output to each input. Therefore, this relation is a function. However, more than one input can have the same output. If we sketch/draw a graph of a relation, and if a vertical line can be drawn that crosses the graph at more than one place, then the relation is not a function

Now, let us consider a function defined by y = f(x)= x². To prepare a graph, we first need to prepare a x-y table to get a set of ordered pairs as under:

x	y
-3	9
-2	4
-1	1
0	0
1	1
2	4
3	9

The ordered pairs can be plotted on a graph paper and smoothly connected.

Alternately, we can use a graphing calculator.

A graph of the function y = f(x)= x² is attached.

The domain , as mentioned earlier is a set of all possible inputs. For example, in case of the function y = f(x)= x², the domain is R, the set of all real numbers. In interval notation, the domain is (-∞,∞).

The range is the set of all possible outputs. For example, in case of the function y = f(x)= x²,the minimum output value is 0 ( the square of a number cannot be negative) and the value of the output increases as x decreases or increase. Therefore, the range of the function y = f(x)= x² is [ 0,∞).

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