Final answer:
The practical range of the function f(x) = 20 + 10x, representing the minutes Jason can play video games based on his study or chore time, is from 20 to 90 minutes. This corresponds to 0 to 7 half-hour increments spent on chores or studies.
Step-by-step explanation:
The question asks us to determine the practical range for the function f(x) = 20 + 10x, which represents the number of minutes Jason can play video games based on the half-hour increments he has done chores or studied. Given that he cannot play for more than 90 minutes a day, we need to find the maximum value of 'x' that would make f(x) equal to 90. The equation would be 20 + 10x = 90. Solving for x, we subtract 20 from both sides, getting 10x = 70, and then divide both sides by 10 to find x = 7. Therefore, the maximum number of half-hour increments Jason can spend on chores or studies to play for 90 minutes is 7, which corresponds to 3.5 hours.
As Jason can only play a minimum of 20 minutes a day, regardless of whether he does chores or studies, and a maximum of 90 minutes, the practical range of the function f(x) is from 20 to 90. So, the function is f(x) = 20 + 10x where 0 ≤ x ≤ 7. The practical range of f(x) is therefore from 20 to 90 minutes.