Question

What is the domain and range of y = 2(x+3)^2 - 1?

Answer 1

Domain: is there any x that you can plug that can make this function undefined?

Answer 2

No?

Answer 3

Tip: as long as there are no fractions or roots, the domain is most likely to be for all numbers.

Answer 4

So the domain here is for all x (all real numbers).

Answer 5

Range: the function is already ordered nicely for you
2(x+3)^2-1
2 would be the coefficient of stretch
3 is the coefficient of left and right
and -1 (the free number) is the coefficient of up and down

Answer 6

So from that alone you can sketch a rough graph of the function.

Answer 7

Okay, so would it be \[(-\infty, \infty)\]

And for range, would it be [-3, infinity)?