Question

The function f has a domain of {10, 13, 15, 17} and a range of (1,3,5).Could f be represented by {(10, 1), (13,3), (13,5), (17, 1))?Justify your answer.

Answer 1

No, it couldn't because:

$\begin{gathered} f(x)\colon\mleft\lbrace(10,1\mright),(13,3),(13,5),(17,1)\} \\ \end{gathered}$

By definition a function f(x) maps an element from one domain to a unique range of elements, so, given a function g(x):

$\begin{gathered} g(x)\colon\mleft\lbrace_{}(x1,y1\mright?),(x2,y2),(x3,y3),\ldots,(xn,yn)\} \\ x1\ne x2\ne x3\ne xn \end{gathered}$

therefore, since:

$\begin{gathered} Let \\ (x2,y2)=(13,3) \\ (x3,y3)=(13,5) \\ x2=x3 \end{gathered}$

It couldn't be a representation of the function