Question

Given no other restrictions, what are the domain and range of the following function?
f(x) = x^2 - 2x + 1

Answer 1

So, you know that the domain is going to be -infinity to infinity

Answer 2

Because you can plug any number in to x and get a result.

Answer 3

^so many students don't understand that concept, though.

Answer 4

You also know right off the bat that its an upward parabola, so it's going to go up, but it's going to have a minimum

Answer 5

Thank you!!

Answer 6

The hard part is finding out what that minimum is.

Answer 7

But if you know how to graph a parabola, you know that the minimum is at 0

Answer 8

So the range is 0 to infinity.

Answer 9

^ the minimum of f(x) = x^2 - 2x + 1 will not be y = 0

First: Find the x-coordinate of the vertex, using x=-b/2a

Answer 10

The plug that into the function to find the minimum y value

Answer 11

Hmm

Answer 12

-(-2)/2(1)

Answer 13

Gives you 1

Answer 14

And at 1, (1)^2 -2(1) + 1

Answer 15

Gives you 0

Answer 16

So I'm pretty sure my range was right?

Answer 17

Turns out it was, but by chance (you didn't know above that it was).

Answer 18

"But if you know how to graph a parabola, you know that the minimum is at 0"
this statement... just because it's a parabola doesn't mean the min is 0

Answer 19

Eh. I just assumed that they knew how to find the vertex of a parabola.