Find the domain and range of the function: f(x)= x^2-10x+7

Question

zehanz · Answer

Domain: all the numbers you can put into f. Now ask yourself this: are there numbers that:
- can't be squared?
- can't be multiplied with -10 and then added 7?

No! so there are no exceptions, the domain is R (all real numbers).

The range is harder. f is a 2nd deg. polynomial, so the graph is a parabola.
The vertex of the parabola is the highest or lowest point, so that sets a boundary for the range.
You will have to find the vertex to get any further with this one.
Do you know how to do that?

anonymous · Answer

-b/2a?

zehanz · Answer

That will do it, you now have to think about whether there is a max or min value for x = -b/2

anonymous · Answer

i think it is a minimum

zehanz · Answer

Right, it is a minimum, value is f(-b/(2a))= f(5) = 25 - 50 + 7 = -18.
So the range is $$[-18, \rightarrow)$$(or some other notation that means the same ;)