Question

Hello,
For a math assignment I have we're supposed to find out if the function f(x) = x^2- 2x + 3 has any of these properties:
-increasing/decreasing
-even/odd
-invertible or not
I said that it was increasing, even, and not invertible, but that was incorrect. Could someone please help?

Answer 1

Also I asked a different Algebra question yesterday(17/6) at around 9 pm and it would be great if someone could offer some ideas on how to solve that algebraically.

Answer 2

You can easily tell that the graph is a parabola which opens up.
f(x) = (x-1)^2 + 2
So, it has a decreasing interval and an increasing interval.
It is decreasing on (-∞,1) and increasing on (1,∞)
You can do that without any calculus. But it's easy to verify since
f'(x) = 2x-2
f' < 0 for x < 1
f' > 0 for x > 1

It is neither even nor odd
not even, since f(-x) ≠ f(x) --- not all powers of x are even
not odd, since f(x) ≠ -f(x) -- not all powers of x are odd

Since it has two branches, it is not invertible unless you restrict the domain.

Answer 3

Oh, I completely forgot that quadratics have both increasing and decreasing intervals! Thank you!