Exercise 8 Page 43

In order to determine the relation between $f(22)$ and $g(22),$ we must find the equation of each function by using the information given in the tables.

Finding the Equation of $f(x)$

The table below gives us some points on the graph of $f(x).$

$x$	$f(x)$
$\text{-}5$	$\text{-}23$
$\text{-}4$	$\text{-}20$
$\text{-}3$	$\text{-}17$
$\text{-}2$	$\text{-}14$

Next, we plot all these points on a coordinate plane.

Now, let's find the equation of the line that passes through $(\text{-}5,\text{-}23)$ and $(\text{-}3,\text{-}17).$ First, we will find its slope. We substitute $(x_1,y_1)=(\text{-}5,\text{-}23)$ and $(x_2,y_2)=(\text{-}3,\text{-}17)$ into the formula above. We can now use the point-slope form $y-y_1=m(x-x_1)$ to find the equation of the line. Therefore, the equation of the function $f(x)$ is $f(x)=3x-8.$ We are ready to find $f(22).$

Finding the Equation of $g(x)$

Now, let's take a look at the right-hand side table, corresponding to $g(x).$

$x$	$g(x)$
$\text{-}2$	$\text{-}18$
$\text{-}1$	$\text{-}14$
$0$	$\text{-}10$
$1$	$\text{-}6$

As before, let's plot these points on a coordinate plane.

This time we already have the $y\text{-}$intercept, namely $b=\text{-}10.$ To find the equation, we will use slope-intercept form. Next, we will use points $(0,\text{-}10)$ and $(1,\text{-}6)$ to find the slope. Consequently, the equation of the function $g(x)$ is $g(x)=4x-10.$ We can now find the value of $g(22).$ After finding both values, we can state the relation between them.