1) The first step of this exercise is to calculate how much were the people's guesses away from the actual number of jelly beans in the jar.
To do so you have to subtract 100 from each guess
Person 1
[tex]85-100=-15[/tex]
→ This difference indicates that the first person's guess was off by 15 pieces less than the actual number of beans
Person 2
[tex]70-100=-30[/tex]
→ This difference indicates that the second person's guess was off by 30 pieces less than the actual number of beans
Person 3
[tex]110-100=10[/tex]
→ This difference indicates that the third person's guess was off by 10 pieces more than the actual number of beans
Person 4
[tex]145-100=45[/tex]
→ This difference indicates that the fourth person's guess was off by 45 pieces more than the actual number of beans
2)
You have to determine a piecewise function that represents the relationship between the absolute value of the difference from the actual count (f(x)) and the person's guess (x)
If the person guessed less than or equal the actual count, x ≤ 100, then you can calculate the absolute difference from the actual count as - x + 100
If the person guessed more than the actual count, x > 100, then you can calculate the absolute difference from the actual count as x - 100
You can express the piecewise function as follows:
[tex]f(x)\begin{cases}-x+100;x\leq100 \\ x-100;x>100\end{cases}[/tex]
3) Now that the function is determined, all that is left is to draw it.
To graph the function, remember that the endpoint of both pieces is 100.
Use the coordinates (85,15) and (70,30) for the first piece and the coordinates (110,10) and (145,45) for the second piece.
