Question 1080639

Function 1:
given points


({{{-4}}},{{{ 0}}}) and ({{{0}}},{{{ 2}}})


use these two points to find slope {{{m}}}:

 {{{m=(2-0)/(0-(-4))=2/4=1/2}}}

now we can find its equation even not necessary to  answer your question


{{{y=(1/2)x+b}}}...use  one point to find  {{{b}}}:

{{{y=(1/2)0+2}}}

{{{y=2}}}

equation is:

{{{y=(1/2)x+2}}}


Function 2
{{{x}}}|{{{ y}}}
{{{2}}}|{{{ 3}}}
{{{3}}}|{{{ 5}}}
{{{4}}}|{{{ 7}}}
{{{5}}}|{{{ 9}}}

{{{y=mx+b}}}........use two points to find slope (rate of change){{{m}}}:

{{{2}}}|{{{ 3}}},{{{3}}}|{{{ 5}}}

 {{{m=(5-3)/(3-2)=2/1=2}}}



{{{y=2x+b}}}.....use  one point to find  {{{b}}}:

{{{4}}}|{{{ 7}}}

{{{7=2*4+b}}}
{{{7=8+b}}}
{{{7-8=b}}}
{{{b=-1}}}

equation is: {{{y=2x-1}}}



Function 1   rate of change is {{{1/2}}} and Function 2   rate of change is {{{2}}}

since {{{2=1/2+3/2}}} , your answer is:

D) Function 2 has a greater rate of change by {{{3/2 }}}