1. ## polynomial question

Write an equation to construct a function whose graph is like that of y=x^2, except for pieces removed for values between 2 and 5, and 7 and 8.

2. Why not just

$\displaystyle f:\{(-\infty, 2)\cup (5, 7) \cup (8, \infty) \to \mathbf{R} | f(x) = x^2\}$?

3. Originally Posted by jasonxl
Write an equation to construct a function whose graph is like that of y=x^2, except for pieces removed for values between 2 and 5, and 7 and 8.
I beleilve this equation would work, although I'm guessing its too complicated to be the equation the question was expecting to be given as an answer:

$\displaystyle y = (x^2)\frac{\sqrt{(x-3)^2-1}}{\sqrt{(x-3)^2-1}}\frac{\sqrt{(x-7.5)^2-\frac{1}{4}}}{\sqrt{(x-7.5)^2-\frac{1}{4}}}$

Again, I beleive this will produce gap bewteen 3 and 5, and a gap between 7 and 8. I hope this helps somehow

4. Actually, the above equation doesnt quite come out correctly, I beleive it has the gaps in the proper places, but I dont think it returns parabolic looking graph otherwise. Its allot to type into a calculator though, so I could've made syntax errors. I think its a step in the right direction though.

EDIT:

I regraphed the above equation, and it looks just like the parabola y=x^2 except for gaps on the intervals

$\displaystyle [3, 5]$

and

$\displaystyle [7, 8]$

I stand by my first equation I posted