Hello, vance!
This is a tricky one!
Luckily, I've done one of these before . . .
A man walks for 45 minutes at a rate of 3 mph, then jogs for 75 minutes at 5 mph,
then sits and rests for 30 minutes, and finally walks for 1 hour and half.
Find the rule of the function that expresses this distance traveled as a function of time. This is a piecewise function.
The distance function depends on what time period is involved.
From , the distance function is: .
. . By the end of the 45 minutes, he has gone 2.25 miles.
From , the distance function is: .
. . By the end of the 75 minutes, he has gone another 6.25 miles, a total of 8.5 miles.
From , the distance function is: .
. . By the end of the 30 minutes, he hasn't moved; his total is still 8.5 miles.
From , the distance function is: .
. . By the end of the 90 minutes, he has gone another 4.5 miles, a total of 13 miles.
The function would be written like this:
. .
The graph would look like this: Code:

 *
 * :
 * :
 * :
 * * * :
 * : : :
 * : : :
 * : : :
 * : : :
 * : : :
 * : : : :
  *   +     +  +      +  
 ¾ 2 2½ 4
