The table shows the imput and output of a function. input 3, 4, 6, 11 output 5, 7, 11, 21 (a) explain what makes this set of data a function. (b) what could cause this set of data to not be a function? provide a specific example to support your statement and explain thoroughly. (c) write and equation, in function motation, that would fit in inputs and outputs in the table. show your work that proves your equation is true fro the given data

Solution:

Table shows input and output value of function.

Input :     3     4     6      11

Output :  5    7     11      21

(a) If we see input and output value of above table. We can see each input get each output. Property of function, if we get different out put for each input value it would be function.

The given data is a set of function.

Domain: {3,4,6,11}

Range: {5,7,11,21}

(b) If we get same output for two different input then it won't be function.

Example:

Input:       2    4      5     8       10

Output:    4    6      8     6        5

We get same output 6 at two different in put 4 and 8. This data won't be a function.

(c)

Input :     3     4     6      11

Output :  5    7     11      21

Formation of function:

f(x)-5=2(x-3)

f(x)=2x-1

Thus, given table id true for function f(x)=2x-1.