Dys-Functional but Rational

As posted on twitter.com/dmarain...

f(x)=(x²-x-6)/(x²-5x+6)
Find x such that f(x)=
0 [-2]
5 [no soln]
1 [no soln]

Answers in brackets

COREFLECTIONS
Fairly traditional rational function question in precalculus? Normally we'd ask students to analyze the function. What was my focus here?

Of course graphing software and CAS systems can be used but students need to walk before they run. The technology helps visualization but, more importantly it allows DIFFERENT, MORE PROBING QUESTIONS to be asked! I'm sure many of you might provide the graph and some key points and ask students to construct a rational function that fits the graph!

So why didn't I simply ask for the zeros, asymptotes, "holes"??