Question 1195888


({{{2}}},{{{5}}}), ({{{4}}},{{{9}}}), ({{{5}}},{{{11}}}), ({{{7}}},{{{15}}}), ({{{10}}},{{{21}}})

A relation is a function if it relates every element in its domain to one and only one element in the range.

Domain:{2,4,5,7,10}
Range:{5,9,11,15,21}

every element in its domain to one and only one element in the range

The list of ordered pairs is a function.

check if  a function is linear


{{{y=mx+b }}}

use (2,5), (4,9) and set up the system

{{{5=m*2+b

{{{5=2m+b ........ .....solve for b

{{{b=5-2m........ eq.1


{{{9=m*4+b }}}

{{{9=4m+b }}} ........ .....solve for {{{b}}}

{{{b=9-4m}}} ........ eq.2


from eq.1 and eq.2 we have


{{{5-2m=9-4m}}} ...... .....solve for {{{m}}}

{{{4m-2m=9-5}}}

{{{ 2m=4}}}

{{{ m=2}}}



{{{b=5-2*2}}}........ eq.1

{{{b=5-4}}}

{{{b=1}}}



a rule that represents the function is


{{{y=2x+1}}}