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Jordan is getting ready for the interclass swimming competition at her school.
She swims to the far end of the pool and comes back to the starting point. The function below models Jordan's distance from the far end of the pool after $t$ seconds.$(II):$ Distribute $1$
$(I), (II):$Distribute $4$
$(I), (II):$ Add terms
Absolute Value Function  Piecewise Function 

$f(x)=4∣∣∣∣∣ 21 +1∣∣∣∣∣ +5$  $f(x)={2x+9,2x+1, ifx<2ifx≥2 $

Start by identifying the absolute value expression.
$(I):$ Distribute $1$
$(I), (II):$Distribute $7$
$(I), (II):$ Add terms
Absolute Value Function  Piecewise Function 

$f(x)=7∣7−x∣+8$  $f(x)={7x+577x−41 ifx>7ifx≤7 $

Comparing this function with the functions written by Dylan and Kriz, it appears that Kriz wrote it correctly.
Finally, these two pieces can be combined on the same coordinate plane.
$f(x)={0.6x+2.40.6x−2.4 if0≤x<4if4≤x≤8 $
$(I), (II):$ Factor out $0.6$
$(I):$ Factor out $1$
$h(x)={0.6x+2.40.6x−2.4 if0≤x<4if4≤x≤8 $
Graph:
$(I):$ Distribute $1$
$(I), (II):$ Distribute $0.6$
$(I), (II):$ Add terms
Since all the measures are in meters, the distance between these two points is $400$ meters.
$(II):$ Distribute $1$
$(I), (II):$ Distribute $3$
$(I), (II):$ Subtract terms