Final answer:
The statement can be represented as the absolute value function |t - 20| ≤ 5, where t is the time in minutes. The function f(t) = |t - 20| models the scenario with a range of 0 ≤ t ≤ 25.
Step-by-step explanation:
To represent the statement "a student estimates that he spent 20 minutes working on his homework, give or take 5 minutes" as an absolute value function, you can write the following expression:
|t - 20| ≤ 5
Here, t represents the actual time spent on homework in minutes. This inequality states that the absolute difference between the estimated time (20 minutes) and the actual time is at most 5 minutes, which captures the estimate's give or take range.
To create an absolute value function that depicts this scenario, we can define the function f(t) as follows:
f(t) = |t - 20|, where 0 ≤ t ≤ 25
This function will graph as a V-shaped figure on a coordinate plane, with the point of the V at (20, 0) and the legs of the V representing the possible deviation from the estimated 20 minutes, within the 5-minute margin.