Looking for a great application of systems of linear inequalities for your Algebra 1 or 2 class? Look no further than today’s GraphJam contribution:
You might just give this picture to students and ask THEM to come up with the equations of the three lines.
There’s also a nice discussion to be had here about inverse functions, or about intersecting lines. And there might also be a good discussion about the domain of reasonableness.
Here are the three functions:
This is especially interesting because I never think of the rule as putting boundaries on a person’s dating age range. Usually people talk about it in the context of “how old of a person can I date?” not “how young of a person can I date?” Or rather, if you’re asking the second question, it’s usually phrased “how young of a person can date me?” (All of these questions relate to functions and their inverses!) But in fact, the half-your-age-plus-seven rule puts a lower and and upper bound on the ages of those you can date.
As far as reasonableness, is it fair to say that my daughter who is 1 can date someone who is between the age of -12 and 7.5? I don’t think so! I’m definitely going to be chasing off those -12 year-olds, I can already tell :-).
For my daughter, the domain of reasonableness might be 
Random Walks 
You daughter can’t date someone between the age of -12 and 8.5. She can date anyone YOUNGER than -12 and anyone OLDER then 8.5. You can easily see this in the graph — the upper limit and lower limit intersect.
You’re totally right… good catch. (actually it’s 7.5…not sure how I missed that, but I’ve corrected it now).
Though it’s also incorrect to say she can date someone outside the range. She can date someone who’s 10, you’re saying. But the 10-year-old can’t date her! Doesn’t make sense. In essence, we’d be saying, “the oldest person you can date is -12 and the youngest person you can date is 7.5,” but no such individuals exist! (we’re asking for both inequalities to be satisfied simultaneously)
She actually can’t date anyone until the intersection point, 14 years old. Despite how crazy the rule seems, it actually makes good sense here. I think no dating before 14 is a pretty good rule!
Thanks again for catching the error, which has produced an even more fruitful discussion!
You’re absolutely right; she can’t date anybody. How could I have missed that!