$In$ this example $we$ considered the function $W=f(T,v),$ where $Wis$ the wind$-$chill index, $Tis$ the actual temperature, and $vis$ the wind speed. A numerical

representation $is$ given $in$ this table.

$(a)$ What $is$ the value $off(-10,50)?$ What $is$ its meaning?

$We$ get $f(-10,50)=$

$,$ which means that $if$ the temperature $is-10C$ and the wind speed $is50k\frac{m}{h}C$ without wind.

$(b)$ Describe $in$ words the meaning $of$ the question "For what value $ofvisf(-20,v)=-30C,$ what wind speed gives a wind$-$chill index $of.$

$C?$

Answer the question.

$v=$

$k\frac{m}{h}$

$(c)$ Describe $in$ words the meaning $of$ the question "For what value $ofTisf(T,20)=-37?"$

The question $is$ asking: when the wind speed $is$

$k\frac{m}{h},$ what temperature gives a wind$-$chill index $of$

$-C?$

Answer the question.

$T=$

$C$

$(d)$ What $is$ the meaning $of$ the function $W=f(-5,v)?$ Describe the behavior $of$ this function.

The function $W=f(-5,v)$ means that $we$ fix $Tat$

and allow $vto$ vary, resulting $in$ a function $of$ one variable. $In$ other words, the

function gives wind$-$chill index values for different wind speeds when the temperature $is$

$CT=-5$ and appears $to$ approach a constant value $asv$ increases.

$(e)$ What $is$ the meaning $of$ the function $W=f(T,40)?$ Describe the behavior $of$ this function.

The function $W=f(T,40)$ means that $we$ fix $vat$

and allow $Tto$ vary, again giving a function $of$ one variable. $In$ other words, the

function gives wind$-$chill index values for different temperatures when the wind speed $is$

$k\frac{m}{h}v=40T$ increases.